Spaces:
Runtime error
Runtime error
File size: 85,729 Bytes
b2af341 1d67a6e b2af341 1d67a6e b2af341 1d67a6e b2af341 1d67a6e b2af341 1d67a6e b2af341 1d67a6e b2af341 3d2ca49 b2af341 1d67a6e b2af341 1d67a6e b2af341 1d67a6e b2af341 3d2ca49 1d67a6e 3d2ca49 1d67a6e 3d2ca49 1d67a6e 3d2ca49 1d67a6e 3d2ca49 1d67a6e 3d2ca49 1d67a6e 3d2ca49 1d67a6e 3d2ca49 1d67a6e 3d2ca49 1d67a6e 3d2ca49 1d67a6e 3d2ca49 1d67a6e 3d2ca49 1d67a6e 3d2ca49 1d67a6e 3d2ca49 1d67a6e 3d2ca49 1d67a6e 3d2ca49 1d67a6e 3d2ca49 1d67a6e 3d2ca49 1d67a6e 3d2ca49 1d67a6e 3d2ca49 1d67a6e 3d2ca49 1d67a6e 3d2ca49 1d67a6e 3d2ca49 1d67a6e 3d2ca49 77ce2b6 1d67a6e 77ce2b6 1d67a6e 77ce2b6 1d67a6e 77ce2b6 1d67a6e 77ce2b6 1d67a6e 77ce2b6 1d67a6e 77ce2b6 1d67a6e 77ce2b6 1d67a6e 77ce2b6 1d67a6e 77ce2b6 1d67a6e 77ce2b6 1d67a6e 77ce2b6 1d67a6e 77ce2b6 1d67a6e 77ce2b6 1d67a6e 77ce2b6 b2af341 1d67a6e b2af341 |
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751 752 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792 793 794 795 796 797 798 799 800 801 802 803 804 805 806 807 808 809 810 811 812 813 814 815 816 817 818 819 820 821 822 823 824 825 826 827 828 829 830 831 832 833 834 835 836 837 838 839 840 841 842 843 844 845 846 847 848 849 850 851 852 853 854 855 856 857 858 859 860 861 862 863 864 865 866 867 868 869 870 871 872 873 874 875 876 877 878 879 880 881 882 883 884 885 886 887 888 889 890 891 892 893 894 895 896 897 898 899 900 901 902 903 904 905 906 907 908 909 910 911 912 913 914 915 916 917 918 919 920 921 922 923 924 925 926 927 928 929 930 931 932 933 934 935 936 937 938 939 940 941 942 943 944 945 946 947 948 949 950 951 952 953 954 955 956 957 958 959 960 961 962 963 964 965 966 967 968 969 970 971 972 973 974 975 976 977 978 979 980 981 982 983 984 985 986 987 988 989 990 991 992 993 994 995 996 997 998 999 1000 1001 1002 1003 1004 1005 1006 1007 1008 1009 1010 1011 1012 1013 1014 1015 1016 1017 1018 1019 1020 1021 1022 1023 1024 1025 1026 1027 1028 1029 1030 1031 1032 1033 1034 1035 1036 1037 1038 1039 1040 1041 1042 1043 1044 1045 1046 1047 1048 1049 1050 1051 1052 1053 1054 1055 1056 1057 1058 1059 1060 1061 1062 1063 1064 1065 1066 1067 1068 1069 1070 1071 1072 1073 1074 1075 1076 1077 1078 1079 1080 1081 1082 1083 1084 1085 1086 1087 1088 1089 1090 1091 1092 1093 1094 1095 1096 1097 1098 1099 1100 1101 1102 1103 1104 1105 1106 1107 1108 1109 1110 1111 1112 1113 1114 1115 1116 1117 1118 1119 1120 1121 1122 1123 1124 1125 1126 1127 1128 1129 1130 1131 1132 1133 1134 1135 1136 1137 1138 1139 1140 1141 1142 1143 1144 1145 1146 1147 1148 1149 1150 1151 1152 1153 1154 1155 1156 1157 1158 1159 1160 1161 1162 1163 1164 1165 1166 1167 1168 1169 1170 1171 1172 1173 1174 1175 1176 1177 1178 1179 1180 1181 1182 1183 1184 1185 1186 1187 1188 1189 1190 1191 1192 1193 1194 1195 1196 1197 1198 1199 1200 1201 1202 1203 1204 1205 1206 1207 1208 1209 1210 1211 1212 1213 1214 1215 1216 1217 1218 1219 1220 1221 1222 1223 1224 1225 1226 1227 1228 1229 1230 1231 |
{
"cells": [
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [],
"source": [
"import importlib"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [],
"source": [
"import pandas as pd\n",
"\n",
"pd.set_option(\"display.max_colwidth\", 0)"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"c:\\Users\\Leems\\Desktop\\Coding\\Projects\\fritz\\venv\\Lib\\site-packages\\tqdm\\auto.py:21: TqdmWarning: IProgress not found. Please update jupyter and ipywidgets. See https://ipywidgets.readthedocs.io/en/stable/user_install.html\n",
" from .autonotebook import tqdm as notebook_tqdm\n"
]
},
{
"data": {
"text/plain": [
"<module 'src.storage' from 'c:\\\\Users\\\\Leems\\\\Desktop\\\\Coding\\\\Projects\\\\fritz\\\\src\\\\storage.py'>"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"import src.embedding as embedding\n",
"import src.storage as storage\n",
"from src.storage import ArXivData\n",
"from src.cleaning import TextCleaner\n",
"from src.embedding import Embedder\n",
"from sentence_transformers import util\n",
"\n",
"importlib.reload(embedding)\n",
"importlib.reload(storage)"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"ename": "PermissionError",
"evalue": "[Errno 13] Permission denied: './data/libraries/APSP_50_allenai-specter/'",
"output_type": "error",
"traceback": [
"\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
"\u001b[1;31mPermissionError\u001b[0m Traceback (most recent call last)",
"Cell \u001b[1;32mIn[8], line 6\u001b[0m\n\u001b[0;32m 3\u001b[0m path_to_library_embeddings \u001b[39m=\u001b[39m \u001b[39m\"\u001b[39m\u001b[39m./data/libraries/APSP_50_allenai-specter/embeddings.feather\u001b[39m\u001b[39m\"\u001b[39m\n\u001b[0;32m 5\u001b[0m library \u001b[39m=\u001b[39m ArXivData()\n\u001b[1;32m----> 6\u001b[0m library\u001b[39m.\u001b[39;49mload_from_feather(library_path)\n",
"File \u001b[1;32mc:\\Users\\Leems\\Desktop\\Coding\\Projects\\fritz\\src\\storage.py:32\u001b[0m, in \u001b[0;36mArXivData.load_from_feather\u001b[1;34m(self, path_to_dataset)\u001b[0m\n\u001b[0;32m 26\u001b[0m \u001b[39mdef\u001b[39;00m \u001b[39mload_from_feather\u001b[39m(\u001b[39mself\u001b[39m, path_to_dataset):\n\u001b[0;32m 27\u001b[0m \u001b[39m \u001b[39m\u001b[39m\"\"\"Loads metadata from a saved feather file.\u001b[39;00m\n\u001b[0;32m 28\u001b[0m \n\u001b[0;32m 29\u001b[0m \u001b[39m Args:\u001b[39;00m\n\u001b[0;32m 30\u001b[0m \u001b[39m path_to_dataset: path to the feather file containing the dataset.\u001b[39;00m\n\u001b[0;32m 31\u001b[0m \u001b[39m \"\"\"\u001b[39;00m\n\u001b[1;32m---> 32\u001b[0m \u001b[39mself\u001b[39m\u001b[39m.\u001b[39m_returned_metadata \u001b[39m=\u001b[39m pd\u001b[39m.\u001b[39;49mread_feather(path_to_dataset)\n\u001b[0;32m 33\u001b[0m \u001b[39mself\u001b[39m\u001b[39m.\u001b[39mmetadata \u001b[39m=\u001b[39m \u001b[39mself\u001b[39m\u001b[39m.\u001b[39m_returned_metadata\n\u001b[0;32m 34\u001b[0m \u001b[39mself\u001b[39m\u001b[39m.\u001b[39marxiv_subjects \u001b[39m=\u001b[39m clean\u001b[39m.\u001b[39mOHE_arxiv_subjects(\u001b[39mself\u001b[39m\u001b[39m.\u001b[39mmetadata)\n",
"File \u001b[1;32mc:\\Users\\Leems\\Desktop\\Coding\\Projects\\fritz\\venv\\Lib\\site-packages\\pandas\\io\\feather_format.py:144\u001b[0m, in \u001b[0;36mread_feather\u001b[1;34m(path, columns, use_threads, storage_options, dtype_backend)\u001b[0m\n\u001b[0;32m 140\u001b[0m \u001b[39mfrom\u001b[39;00m \u001b[39mpyarrow\u001b[39;00m \u001b[39mimport\u001b[39;00m feather\n\u001b[0;32m 142\u001b[0m check_dtype_backend(dtype_backend)\n\u001b[1;32m--> 144\u001b[0m \u001b[39mwith\u001b[39;00m get_handle(\n\u001b[0;32m 145\u001b[0m path, \u001b[39m\"\u001b[39;49m\u001b[39mrb\u001b[39;49m\u001b[39m\"\u001b[39;49m, storage_options\u001b[39m=\u001b[39;49mstorage_options, is_text\u001b[39m=\u001b[39;49m\u001b[39mFalse\u001b[39;49;00m\n\u001b[0;32m 146\u001b[0m ) \u001b[39mas\u001b[39;00m handles:\n\u001b[0;32m 147\u001b[0m \u001b[39mif\u001b[39;00m dtype_backend \u001b[39mis\u001b[39;00m lib\u001b[39m.\u001b[39mno_default:\n\u001b[0;32m 148\u001b[0m \u001b[39mreturn\u001b[39;00m feather\u001b[39m.\u001b[39mread_feather(\n\u001b[0;32m 149\u001b[0m handles\u001b[39m.\u001b[39mhandle, columns\u001b[39m=\u001b[39mcolumns, use_threads\u001b[39m=\u001b[39m\u001b[39mbool\u001b[39m(use_threads)\n\u001b[0;32m 150\u001b[0m )\n",
"File \u001b[1;32mc:\\Users\\Leems\\Desktop\\Coding\\Projects\\fritz\\venv\\Lib\\site-packages\\pandas\\io\\common.py:868\u001b[0m, in \u001b[0;36mget_handle\u001b[1;34m(path_or_buf, mode, encoding, compression, memory_map, is_text, errors, storage_options)\u001b[0m\n\u001b[0;32m 859\u001b[0m handle \u001b[39m=\u001b[39m \u001b[39mopen\u001b[39m(\n\u001b[0;32m 860\u001b[0m handle,\n\u001b[0;32m 861\u001b[0m ioargs\u001b[39m.\u001b[39mmode,\n\u001b[1;32m (...)\u001b[0m\n\u001b[0;32m 864\u001b[0m newline\u001b[39m=\u001b[39m\u001b[39m\"\u001b[39m\u001b[39m\"\u001b[39m,\n\u001b[0;32m 865\u001b[0m )\n\u001b[0;32m 866\u001b[0m \u001b[39melse\u001b[39;00m:\n\u001b[0;32m 867\u001b[0m \u001b[39m# Binary mode\u001b[39;00m\n\u001b[1;32m--> 868\u001b[0m handle \u001b[39m=\u001b[39m \u001b[39mopen\u001b[39;49m(handle, ioargs\u001b[39m.\u001b[39;49mmode)\n\u001b[0;32m 869\u001b[0m handles\u001b[39m.\u001b[39mappend(handle)\n\u001b[0;32m 871\u001b[0m \u001b[39m# Convert BytesIO or file objects passed with an encoding\u001b[39;00m\n",
"\u001b[1;31mPermissionError\u001b[0m: [Errno 13] Permission denied: './data/libraries/APSP_50_allenai-specter/'"
]
}
],
"source": [
"## Load library\n",
"library_path = \"./data/libraries/APSP_50_allenai-specter/\"\n",
"path_to_library_embeddings = (\n",
" \"./data/libraries/APSP_50_allenai-specter/embeddings.feather\"\n",
")\n",
"\n",
"library = ArXivData()\n",
"library.load_from_feather(library_path)"
]
},
{
"cell_type": "code",
"execution_count": 40,
"metadata": {},
"outputs": [],
"source": [
"## Prepare the Library\n",
"\n",
"cleaner = TextCleaner()\n",
"embedder = Embedder()\n",
"\n",
"clean_library = cleaner.transform(library)\n",
"prepped_library = embedder.transform(\n",
" X=clean_library, load_from_file=True, path_to_embeddings=path_to_library_embeddings\n",
")"
]
},
{
"cell_type": "code",
"execution_count": 48,
"metadata": {},
"outputs": [],
"source": [
"## retrieve and pre-process the input\n",
"\n",
"input_id = \"1602.00730\"\n",
"\n",
"## create query string\n",
"\n",
"id_list = [input_id]\n",
"\n",
"input_article = ArXivData()\n",
"input_article.load_from_id_list(id_list=id_list)"
]
},
{
"cell_type": "code",
"execution_count": 49,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"c:\\Users\\Leems\\Desktop\\Coding\\Projects\\Fritz\\cleaning.py:23: SettingWithCopyWarning: \n",
"A value is trying to be set on a copy of a slice from a DataFrame\n",
"\n",
"See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n",
" X.metadata.msc_tags[X.metadata.msc_tags.notna()] = X.metadata.msc_tags[\n",
"Batches: 100%|██████████| 1/1 [00:00<00:00, 4.39it/s]\n"
]
}
],
"source": [
"## Clean and process the input\n",
"\n",
"clean_input_article = cleaner.transform(input_article)\n",
"prepped_input_article = embedder.transform(\n",
" X=clean_input_article,\n",
" model_name=\"allenai-specter\",\n",
" path_to_embeddings=\"./data/input_embedding.feather\",\n",
")"
]
},
{
"cell_type": "code",
"execution_count": 55,
"metadata": {},
"outputs": [],
"source": [
"## Perform the search and return the closest matches\n",
"\n",
"matches = util.semantic_search(\n",
" query_embeddings=prepped_input_article.embeddings,\n",
" corpus_embeddings=prepped_library.embeddings,\n",
" top_k=5,\n",
")"
]
},
{
"cell_type": "code",
"execution_count": 57,
"metadata": {},
"outputs": [],
"source": [
"indices = [dict[\"corpus_id\"] for dict in matches[0]]"
]
},
{
"cell_type": "code",
"execution_count": 59,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[38787, 39127, 9786, 49609, 14857]"
]
},
"execution_count": 59,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"indices"
]
},
{
"cell_type": "code",
"execution_count": 60,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<style scoped>\n",
" .dataframe tbody tr th:only-of-type {\n",
" vertical-align: middle;\n",
" }\n",
"\n",
" .dataframe tbody tr th {\n",
" vertical-align: top;\n",
" }\n",
"\n",
" .dataframe thead th {\n",
" text-align: right;\n",
" }\n",
"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>title</th>\n",
" <th>abstract</th>\n",
" <th>id</th>\n",
" <th>arxiv_subjects</th>\n",
" <th>msc_tags</th>\n",
" <th>doc_strings</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>38787</th>\n",
" <td>C-infinity Scaling Asymptotics for the Spectral Function of the Laplacian</td>\n",
" <td>This article concerns new off-diagonal estimates on the remainder and its derivatives in the pointwise Weyl law on a compact n-dimensional Riemannian manifold. As an application, we prove that near any non self-focal point, the scaling limit of the spectral projector of the Laplacian onto frequency windows of constant size is a normalized Bessel function depending only on n.</td>\n",
" <td>1602.00730v1</td>\n",
" <td>[math.AP, math-ph, math.DG, math.FA, math.MP, math.SP]</td>\n",
" <td>None</td>\n",
" <td>C-infinity Scaling Asymptotics for the Spectral Function of the Laplacian This article concerns new off-diagonal estimates on the remainder and its derivatives in the pointwise Weyl law on a compact n-dimensional Riemannian manifold. As an application, we prove that near any non self-focal point, the scaling limit of the spectral projector of the Laplacian onto frequency windows of constant size is a normalized Bessel function depending only on n.</td>\n",
" </tr>\n",
" <tr>\n",
" <th>39127</th>\n",
" <td>Scaling Limit for the Kernel of the Spectral Projector and Remainder Estimates in the Pointwise Weyl Law</td>\n",
" <td>Let (M, g) be a compact smooth Riemannian manifold. We obtain new off-diagonal estimates as {ambda} tend to infinity for the remainder in the pointwise Weyl Law for the kernel of the spectral projector of the Laplacian onto functions with frequency at most {ambda}. A corollary is that, when rescaled around a non self-focal point, the kernel of the spectral projector onto the frequency interval (ambda, ambda + 1] has a universal scaling limit as {ambda} goes to infinity (depending only on the dimension of M). Our results also imply that if M has no conjugate points, then immersions of M into Euclidean space by an orthonormal basis of eigenfunctions with frequencies in (ambda, ambda + 1] are embeddings for all {ambda} sufficiently large.</td>\n",
" <td>1411.0658v3</td>\n",
" <td>[math.SP, math.AP, math.DG]</td>\n",
" <td>None</td>\n",
" <td>Scaling Limit for the Kernel of the Spectral Projector and Remainder Estimates in the Pointwise Weyl Law Let (M, g) be a compact smooth Riemannian manifold. We obtain new off-diagonal estimates as {ambda} tend to infinity for the remainder in the pointwise Weyl Law for the kernel of the spectral projector of the Laplacian onto functions with frequency at most {ambda}. A corollary is that, when rescaled around a non self-focal point, the kernel of the spectral projector onto the frequency interval (ambda, ambda + 1] has a universal scaling limit as {ambda} goes to infinity (depending only on the dimension of M). Our results also imply that if M has no conjugate points, then immersions of M into Euclidean space by an orthonormal basis of eigenfunctions with frequencies in (ambda, ambda + 1] are embeddings for all {ambda} sufficiently large.</td>\n",
" </tr>\n",
" <tr>\n",
" <th>9786</th>\n",
" <td>A logarithmic improvement in the two-point Weyl law for manifolds without conjugate points</td>\n",
" <td>In this paper, we study the two-point Weyl Law for the Laplace-Beltrami operator on a smooth, compact Riemannian manifold LATEX with no conjugate points. That is, we find the asymptotic behavior of the Schwartz kernel, LATEX of the projection operator from LATEX onto the direct sum of eigenspaces with eigenvalue smaller than LATEX as LATEX In the regime where LATEX are restricted to a compact neighborhood of the diagonal in LATEX we obtain a uniform logarithmic improvement in the remainder of the asymptotic expansion for LATEX and its derivatives of all orders, which generalizes a result of Berard, who treated the on-diagonal case LATEX When LATEX avoid a compact neighborhood of the diagonal, we obtain this same improvement in an upper bound for LATEX Our results imply that the rescaled covariance kernel of a monochromatic random wave locally converges in the LATEX topology to a universal scaling limit at an inverse logarithmic rate.</td>\n",
" <td>1905.05136v3</td>\n",
" <td>[math.AP, math.SP]</td>\n",
" <td>[Asymptotic distributions of eigenvalues in context of PDEs]</td>\n",
" <td>A logarithmic improvement in the two-point Weyl law for manifolds without conjugate points In this paper, we study the two-point Weyl Law for the Laplace-Beltrami operator on a smooth, compact Riemannian manifold LATEX with no conjugate points. That is, we find the asymptotic behavior of the Schwartz kernel, LATEX of the projection operator from LATEX onto the direct sum of eigenspaces with eigenvalue smaller than LATEX as LATEX In the regime where LATEX are restricted to a compact neighborhood of the diagonal in LATEX we obtain a uniform logarithmic improvement in the remainder of the asymptotic expansion for LATEX and its derivatives of all orders, which generalizes a result of Berard, who treated the on-diagonal case LATEX When LATEX avoid a compact neighborhood of the diagonal, we obtain this same improvement in an upper bound for LATEX Our results imply that the rescaled covariance kernel of a monochromatic random wave locally converges in the LATEX topology to a universal scaling limit at an inverse logarithmic rate.</td>\n",
" </tr>\n",
" <tr>\n",
" <th>49609</th>\n",
" <td>The blowup along the diagonal of the spectral function of the Laplacian</td>\n",
" <td>We formulate a precise conjecture about the universal behavior near the diagonal of the spectral function of the Laplacian of a smooth compact Riemann manifold. We prove this conjecture when the manifold and the metric are real analytic, and we also present an alternate proof when the manifold is the round sphere.</td>\n",
" <td>1103.1276v4</td>\n",
" <td>[math.DG, math-ph, math.AP, math.MP]</td>\n",
" <td>[Spectral problems; spectral geometry; scattering theory on manifolds, Second-order elliptic equations]</td>\n",
" <td>The blowup along the diagonal of the spectral function of the Laplacian We formulate a precise conjecture about the universal behavior near the diagonal of the spectral function of the Laplacian of a smooth compact Riemann manifold. We prove this conjecture when the manifold and the metric are real analytic, and we also present an alternate proof when the manifold is the round sphere.</td>\n",
" </tr>\n",
" <tr>\n",
" <th>14857</th>\n",
" <td>Growth of high LATEX norms for eigenfunctions: an application of geodesic beams</td>\n",
" <td>This work concerns LATEX norms of high energy Laplace eigenfunctions, LATEX LATEX In 1988, Sogge gave optimal estimates on the growth of LATEX for a general compact Riemannian manifold. The goal of this article is to give general dynamical conditions guaranteeing quantitative improvements in LATEX estimates for LATEX where LATEX is the critical exponent. We also apply previous results of the authors to obtain quantitative improvements in concrete geometric settings including all product manifolds. These are the first results improving estimates for the LATEX growth of eigenfunctions that only require dynamical assumptions. In contrast with previous improvements, our assumptions are local in the sense that they depend only on the geodesics passing through a shrinking neighborhood of a given set in LATEX Moreover, the article gives a structure theorem for eigenfunctions which saturate the quantitatively improved LATEX bound. Modulo an error, the theorem describes these eigenfunctions as finite sums of quasimodes which, roughly, approximate zonal harmonics on the sphere scaled by LATEX</td>\n",
" <td>2003.04597v2</td>\n",
" <td>[math.AP, math.SP]</td>\n",
" <td>None</td>\n",
" <td>Growth of high LATEX norms for eigenfunctions: an application of geodesic beams This work concerns LATEX norms of high energy Laplace eigenfunctions, LATEX LATEX In 1988, Sogge gave optimal estimates on the growth of LATEX for a general compact Riemannian manifold. The goal of this article is to give general dynamical conditions guaranteeing quantitative improvements in LATEX estimates for LATEX where LATEX is the critical exponent. We also apply previous results of the authors to obtain quantitative improvements in concrete geometric settings including all product manifolds. These are the first results improving estimates for the LATEX growth of eigenfunctions that only require dynamical assumptions. In contrast with previous improvements, our assumptions are local in the sense that they depend only on the geodesics passing through a shrinking neighborhood of a given set in LATEX Moreover, the article gives a structure theorem for eigenfunctions which saturate the quantitatively improved LATEX bound. Modulo an error, the theorem describes these eigenfunctions as finite sums of quasimodes which, roughly, approximate zonal harmonics on the sphere scaled by LATEX</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" title \\\n",
"38787 C-infinity Scaling Asymptotics for the Spectral Function of the Laplacian \n",
"39127 Scaling Limit for the Kernel of the Spectral Projector and Remainder Estimates in the Pointwise Weyl Law \n",
"9786 A logarithmic improvement in the two-point Weyl law for manifolds without conjugate points \n",
"49609 The blowup along the diagonal of the spectral function of the Laplacian \n",
"14857 Growth of high LATEX norms for eigenfunctions: an application of geodesic beams \n",
"\n",
" abstract \\\n",
"38787 This article concerns new off-diagonal estimates on the remainder and its derivatives in the pointwise Weyl law on a compact n-dimensional Riemannian manifold. As an application, we prove that near any non self-focal point, the scaling limit of the spectral projector of the Laplacian onto frequency windows of constant size is a normalized Bessel function depending only on n. \n",
"39127 Let (M, g) be a compact smooth Riemannian manifold. We obtain new off-diagonal estimates as {ambda} tend to infinity for the remainder in the pointwise Weyl Law for the kernel of the spectral projector of the Laplacian onto functions with frequency at most {ambda}. A corollary is that, when rescaled around a non self-focal point, the kernel of the spectral projector onto the frequency interval (ambda, ambda + 1] has a universal scaling limit as {ambda} goes to infinity (depending only on the dimension of M). Our results also imply that if M has no conjugate points, then immersions of M into Euclidean space by an orthonormal basis of eigenfunctions with frequencies in (ambda, ambda + 1] are embeddings for all {ambda} sufficiently large. \n",
"9786 In this paper, we study the two-point Weyl Law for the Laplace-Beltrami operator on a smooth, compact Riemannian manifold LATEX with no conjugate points. That is, we find the asymptotic behavior of the Schwartz kernel, LATEX of the projection operator from LATEX onto the direct sum of eigenspaces with eigenvalue smaller than LATEX as LATEX In the regime where LATEX are restricted to a compact neighborhood of the diagonal in LATEX we obtain a uniform logarithmic improvement in the remainder of the asymptotic expansion for LATEX and its derivatives of all orders, which generalizes a result of Berard, who treated the on-diagonal case LATEX When LATEX avoid a compact neighborhood of the diagonal, we obtain this same improvement in an upper bound for LATEX Our results imply that the rescaled covariance kernel of a monochromatic random wave locally converges in the LATEX topology to a universal scaling limit at an inverse logarithmic rate. \n",
"49609 We formulate a precise conjecture about the universal behavior near the diagonal of the spectral function of the Laplacian of a smooth compact Riemann manifold. We prove this conjecture when the manifold and the metric are real analytic, and we also present an alternate proof when the manifold is the round sphere. \n",
"14857 This work concerns LATEX norms of high energy Laplace eigenfunctions, LATEX LATEX In 1988, Sogge gave optimal estimates on the growth of LATEX for a general compact Riemannian manifold. The goal of this article is to give general dynamical conditions guaranteeing quantitative improvements in LATEX estimates for LATEX where LATEX is the critical exponent. We also apply previous results of the authors to obtain quantitative improvements in concrete geometric settings including all product manifolds. These are the first results improving estimates for the LATEX growth of eigenfunctions that only require dynamical assumptions. In contrast with previous improvements, our assumptions are local in the sense that they depend only on the geodesics passing through a shrinking neighborhood of a given set in LATEX Moreover, the article gives a structure theorem for eigenfunctions which saturate the quantitatively improved LATEX bound. Modulo an error, the theorem describes these eigenfunctions as finite sums of quasimodes which, roughly, approximate zonal harmonics on the sphere scaled by LATEX \n",
"\n",
" id arxiv_subjects \\\n",
"38787 1602.00730v1 [math.AP, math-ph, math.DG, math.FA, math.MP, math.SP] \n",
"39127 1411.0658v3 [math.SP, math.AP, math.DG] \n",
"9786 1905.05136v3 [math.AP, math.SP] \n",
"49609 1103.1276v4 [math.DG, math-ph, math.AP, math.MP] \n",
"14857 2003.04597v2 [math.AP, math.SP] \n",
"\n",
" msc_tags \\\n",
"38787 None \n",
"39127 None \n",
"9786 [Asymptotic distributions of eigenvalues in context of PDEs] \n",
"49609 [Spectral problems; spectral geometry; scattering theory on manifolds, Second-order elliptic equations] \n",
"14857 None \n",
"\n",
" doc_strings \n",
"38787 C-infinity Scaling Asymptotics for the Spectral Function of the Laplacian This article concerns new off-diagonal estimates on the remainder and its derivatives in the pointwise Weyl law on a compact n-dimensional Riemannian manifold. As an application, we prove that near any non self-focal point, the scaling limit of the spectral projector of the Laplacian onto frequency windows of constant size is a normalized Bessel function depending only on n. \n",
"39127 Scaling Limit for the Kernel of the Spectral Projector and Remainder Estimates in the Pointwise Weyl Law Let (M, g) be a compact smooth Riemannian manifold. We obtain new off-diagonal estimates as {ambda} tend to infinity for the remainder in the pointwise Weyl Law for the kernel of the spectral projector of the Laplacian onto functions with frequency at most {ambda}. A corollary is that, when rescaled around a non self-focal point, the kernel of the spectral projector onto the frequency interval (ambda, ambda + 1] has a universal scaling limit as {ambda} goes to infinity (depending only on the dimension of M). Our results also imply that if M has no conjugate points, then immersions of M into Euclidean space by an orthonormal basis of eigenfunctions with frequencies in (ambda, ambda + 1] are embeddings for all {ambda} sufficiently large. \n",
"9786 A logarithmic improvement in the two-point Weyl law for manifolds without conjugate points In this paper, we study the two-point Weyl Law for the Laplace-Beltrami operator on a smooth, compact Riemannian manifold LATEX with no conjugate points. That is, we find the asymptotic behavior of the Schwartz kernel, LATEX of the projection operator from LATEX onto the direct sum of eigenspaces with eigenvalue smaller than LATEX as LATEX In the regime where LATEX are restricted to a compact neighborhood of the diagonal in LATEX we obtain a uniform logarithmic improvement in the remainder of the asymptotic expansion for LATEX and its derivatives of all orders, which generalizes a result of Berard, who treated the on-diagonal case LATEX When LATEX avoid a compact neighborhood of the diagonal, we obtain this same improvement in an upper bound for LATEX Our results imply that the rescaled covariance kernel of a monochromatic random wave locally converges in the LATEX topology to a universal scaling limit at an inverse logarithmic rate. \n",
"49609 The blowup along the diagonal of the spectral function of the Laplacian We formulate a precise conjecture about the universal behavior near the diagonal of the spectral function of the Laplacian of a smooth compact Riemann manifold. We prove this conjecture when the manifold and the metric are real analytic, and we also present an alternate proof when the manifold is the round sphere. \n",
"14857 Growth of high LATEX norms for eigenfunctions: an application of geodesic beams This work concerns LATEX norms of high energy Laplace eigenfunctions, LATEX LATEX In 1988, Sogge gave optimal estimates on the growth of LATEX for a general compact Riemannian manifold. The goal of this article is to give general dynamical conditions guaranteeing quantitative improvements in LATEX estimates for LATEX where LATEX is the critical exponent. We also apply previous results of the authors to obtain quantitative improvements in concrete geometric settings including all product manifolds. These are the first results improving estimates for the LATEX growth of eigenfunctions that only require dynamical assumptions. In contrast with previous improvements, our assumptions are local in the sense that they depend only on the geodesics passing through a shrinking neighborhood of a given set in LATEX Moreover, the article gives a structure theorem for eigenfunctions which saturate the quantitatively improved LATEX bound. Modulo an error, the theorem describes these eigenfunctions as finite sums of quasimodes which, roughly, approximate zonal harmonics on the sphere scaled by LATEX "
]
},
"execution_count": 60,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"## Retrieve indices\n",
"\n",
"prepped_library._returned_metadata.iloc[indices]"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {},
"outputs": [],
"source": [
"id_list = [\"1602.00730\"]"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<module 'src.search' from 'c:\\\\Users\\\\Leems\\\\Desktop\\\\Coding\\\\Projects\\\\fritz\\\\src\\\\search.py'>"
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"import src.embedding as embedding\n",
"import src.search as search\n",
"import importlib\n",
"from src.storage import Fetch\n",
"from src.cleaning import TextCleaner\n",
"from src.embedding import Embedder\n",
"from src.search import Search\n",
"\n",
"importlib.reload(embedding)\n",
"importlib.reload(search)"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"ename": "NameError",
"evalue": "name 'id_list' is not defined",
"output_type": "error",
"traceback": [
"\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
"\u001b[1;31mNameError\u001b[0m Traceback (most recent call last)",
"Cell \u001b[1;32mIn[11], line 3\u001b[0m\n\u001b[0;32m 1\u001b[0m \u001b[39m## Fetch metadata of input\u001b[39;00m\n\u001b[0;32m 2\u001b[0m getter \u001b[39m=\u001b[39m Fetch()\n\u001b[1;32m----> 3\u001b[0m into_cleaner \u001b[39m=\u001b[39m getter\u001b[39m.\u001b[39mtransform(X\u001b[39m=\u001b[39mid_list)\n",
"\u001b[1;31mNameError\u001b[0m: name 'id_list' is not defined"
]
}
],
"source": [
"## Fetch metadata of input\n",
"getter = Fetch()\n",
"into_cleaner = getter.transform(X=id_list)"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"ename": "NameError",
"evalue": "name 'into_cleaner' is not defined",
"output_type": "error",
"traceback": [
"\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
"\u001b[1;31mNameError\u001b[0m Traceback (most recent call last)",
"Cell \u001b[1;32mIn[12], line 3\u001b[0m\n\u001b[0;32m 1\u001b[0m cleaner \u001b[39m=\u001b[39m TextCleaner()\n\u001b[1;32m----> 3\u001b[0m into_embedder \u001b[39m=\u001b[39m cleaner\u001b[39m.\u001b[39mtransform(into_cleaner)\n",
"\u001b[1;31mNameError\u001b[0m: name 'into_cleaner' is not defined"
]
}
],
"source": [
"cleaner = TextCleaner()\n",
"\n",
"into_embedder = cleaner.transform(into_cleaner)"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [
{
"ename": "NameError",
"evalue": "name 'into_embedder' is not defined",
"output_type": "error",
"traceback": [
"\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
"\u001b[1;31mNameError\u001b[0m Traceback (most recent call last)",
"Cell \u001b[1;32mIn[13], line 2\u001b[0m\n\u001b[0;32m 1\u001b[0m embedder \u001b[39m=\u001b[39m Embedder(model_name\u001b[39m=\u001b[39m\u001b[39m\"\u001b[39m\u001b[39mallenai-specter\u001b[39m\u001b[39m\"\u001b[39m)\n\u001b[1;32m----> 2\u001b[0m into_search \u001b[39m=\u001b[39m embedder\u001b[39m.\u001b[39mtransform(into_embedder)\n",
"\u001b[1;31mNameError\u001b[0m: name 'into_embedder' is not defined"
]
}
],
"source": [
"embedder = Embedder(model_name=\"allenai-specter\")\n",
"into_search = embedder.transform(into_embedder)"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [
{
"ename": "NameError",
"evalue": "name 'into_search' is not defined",
"output_type": "error",
"traceback": [
"\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
"\u001b[1;31mNameError\u001b[0m Traceback (most recent call last)",
"Cell \u001b[1;32mIn[14], line 3\u001b[0m\n\u001b[0;32m 1\u001b[0m search \u001b[39m=\u001b[39m Search(path_to_library\u001b[39m=\u001b[39m\u001b[39m\"\u001b[39m\u001b[39m./data/libraries/APSP_50_allenai-specter/\u001b[39m\u001b[39m\"\u001b[39m)\n\u001b[1;32m----> 3\u001b[0m search\u001b[39m.\u001b[39mtransform(X\u001b[39m=\u001b[39minto_search)\u001b[39m.\u001b[39mid\u001b[39m.\u001b[39mto_list()\n",
"\u001b[1;31mNameError\u001b[0m: name 'into_search' is not defined"
]
}
],
"source": [
"search = Search(path_to_library=\"./data/libraries/APSP_50_allenai-specter/\")\n",
"\n",
"search.transform(X=into_search).id.to_list()"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [
{
"ename": "NameError",
"evalue": "name 'id_list' is not defined",
"output_type": "error",
"traceback": [
"\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
"\u001b[1;31mNameError\u001b[0m Traceback (most recent call last)",
"Cell \u001b[1;32mIn[15], line 13\u001b[0m\n\u001b[0;32m 1\u001b[0m \u001b[39mfrom\u001b[39;00m \u001b[39msklearn\u001b[39;00m\u001b[39m.\u001b[39;00m\u001b[39mpipeline\u001b[39;00m \u001b[39mimport\u001b[39;00m Pipeline\n\u001b[0;32m 3\u001b[0m pipe \u001b[39m=\u001b[39m Pipeline(\n\u001b[0;32m 4\u001b[0m [\n\u001b[0;32m 5\u001b[0m (\u001b[39m\"\u001b[39m\u001b[39mfetch\u001b[39m\u001b[39m\"\u001b[39m, Fetch()),\n\u001b[1;32m (...)\u001b[0m\n\u001b[0;32m 9\u001b[0m ]\n\u001b[0;32m 10\u001b[0m )\n\u001b[1;32m---> 13\u001b[0m pipe\u001b[39m.\u001b[39mtransform(X\u001b[39m=\u001b[39mid_list)\n",
"\u001b[1;31mNameError\u001b[0m: name 'id_list' is not defined"
]
}
],
"source": [
"from sklearn.pipeline import Pipeline\n",
"\n",
"pipe = Pipeline(\n",
" [\n",
" (\"fetch\", Fetch()),\n",
" (\"clean\", TextCleaner()),\n",
" (\"embed\", Embedder(model_name=\"allenai-specter\")),\n",
" (\"search\", Search(path_to_library=\"./data/libraries/APSP_50_allenai-specter/\")),\n",
" ]\n",
")\n",
"\n",
"\n",
"pipe.transform(X=id_list)"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [],
"source": [
"import src.model\n",
"import importlib\n",
"\n",
"importlib.reload(src.model)\n",
"from src.model import main"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<style scoped>\n",
" .dataframe tbody tr th:only-of-type {\n",
" vertical-align: middle;\n",
" }\n",
"\n",
" .dataframe tbody tr th {\n",
" vertical-align: top;\n",
" }\n",
"\n",
" .dataframe thead th {\n",
" text-align: right;\n",
" }\n",
"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>title</th>\n",
" <th>abstract</th>\n",
" <th>id</th>\n",
" <th>arxiv_subjects</th>\n",
" <th>msc_tags</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>9786</th>\n",
" <td>A logarithmic improvement in the two-point Weyl law for manifolds without conjugate points</td>\n",
" <td>In this paper, we study the two-point Weyl Law for the Laplace-Beltrami\\noperator on a smooth, compact Riemannian manifold $M$ with no conjugate points.\\nThat is, we find the asymptotic behavior of the Schwartz kernel,\\n$E_\\lambda(x,y)$, of the projection operator from $L^2(M)$ onto the direct sum\\nof eigenspaces with eigenvalue smaller than $\\lambda^2$ as $\\lambda \\to\\infty$.\\nIn the regime where $x,y$ are restricted to a compact neighborhood of the\\ndiagonal in $M\\times M$, we obtain a uniform logarithmic improvement in the\\nremainder of the asymptotic expansion for $E_\\lambda$ and its derivatives of\\nall orders, which generalizes a result of B\\'erard, who treated the on-diagonal\\ncase $E_\\lambda(x,x)$. When $x,y$ avoid a compact neighborhood of the diagonal,\\nwe obtain this same improvement in an upper bound for $E_\\lambda$. Our results\\nimply that the rescaled covariance kernel of a monochromatic random wave\\nlocally converges in the $C^\\infty$ topology to a universal scaling limit at an\\ninverse logarithmic rate.</td>\n",
" <td>1905.05136v3</td>\n",
" <td>[math.AP, math.SP]</td>\n",
" <td>[35P20]</td>\n",
" </tr>\n",
" <tr>\n",
" <th>39127</th>\n",
" <td>Scaling Limit for the Kernel of the Spectral Projector and Remainder Estimates in the Pointwise Weyl Law</td>\n",
" <td>Let (M, g) be a compact smooth Riemannian manifold. We obtain new\\noff-diagonal estimates as {\\lambda} tend to infinity for the remainder in the\\npointwise Weyl Law for the kernel of the spectral projector of the Laplacian\\nonto functions with frequency at most {\\lambda}. A corollary is that, when\\nrescaled around a non self-focal point, the kernel of the spectral projector\\nonto the frequency interval (\\lambda, \\lambda + 1] has a universal scaling\\nlimit as {\\lambda} goes to infinity (depending only on the dimension of M). Our\\nresults also imply that if M has no conjugate points, then immersions of M into\\nEuclidean space by an orthonormal basis of eigenfunctions with frequencies in\\n(\\lambda, \\lambda + 1] are embeddings for all {\\lambda} sufficiently large.</td>\n",
" <td>1411.0658v3</td>\n",
" <td>[math.SP, math.AP, math.DG]</td>\n",
" <td>None</td>\n",
" </tr>\n",
" <tr>\n",
" <th>46524</th>\n",
" <td>On $L^p$-resolvent estimates and the density of eigenvalues for compact Riemannian manifolds</td>\n",
" <td>We address an interesting question raised by Dos Santos Ferreira, Kenig and\\nSalo about regions ${\\mathcal R}_g\\subset {\\mathbb C}$ for which there can be\\nuniform $L^{\\frac{2n}{n+2}}\\to L^{\\frac{2n}{n-2}}$ resolvent estimates for\\n$\\Delta_g+\\zeta$, $\\zeta \\in {\\mathcal R}_g$, where $\\Delta_g$ is the\\nLaplace-Beltrami operator with metric $g$ on a given compact boundaryless\\nRiemannian manifold of dimension $n\\ge3$. This is related to earlier work of\\nKenig, Ruiz and the third author for the Euclidean Laplacian, in which case the\\nregion is the entire complex plane minus any disc centered at the origin.\\nPresently, we show that for the round metric on the sphere, $S^n$, the\\nresolvent estimates in Ferreira et al, involving a much smaller region, are\\nessentially optimal. We do this by establishing sharp bounds based on the\\ndistance from $\\zeta$ to the spectrum of $\\Delta_{S^n}$.\\n In the other direction, we also show that the bounds in \\cite{Kenig} can be\\nsharpened logarithmically for manifolds with nonpositive curvature, and by\\npowers in the case of the torus, ${\\mathbb T}^n={\\mathbb R}^n/{\\mathbb Z}^n$,\\nwith the flat metric. The latter improves earlier bounds of Shen.\\n Further improvements for the torus are obtained using recent techniques of\\nthe first author and his work with Guth based on the multilinear estimates of\\nBennett, Carbery and Tao. Our approach also allows us to give a natural\\nnecessary condition for favorable resolvent estimates that is based on a\\nmeasurement of the density of the spectrum of $\\sqrt{-\\Delta_g}$, and,\\nmoreover, a necessary and sufficient condition based on natural improved\\nspectral projection estimates for shrinking intervals.</td>\n",
" <td>1204.3927v3</td>\n",
" <td>[math.AP, math.CA]</td>\n",
" <td>[58J50]</td>\n",
" </tr>\n",
" <tr>\n",
" <th>38787</th>\n",
" <td>C-infinity Scaling Asymptotics for the Spectral Function of the Laplacian</td>\n",
" <td>This article concerns new off-diagonal estimates on the remainder and its\\nderivatives in the pointwise Weyl law on a compact n-dimensional Riemannian\\nmanifold. As an application, we prove that near any non self-focal point, the\\nscaling limit of the spectral projector of the Laplacian onto frequency windows\\nof constant size is a normalized Bessel function depending only on n.</td>\n",
" <td>1602.00730v1</td>\n",
" <td>[math.AP, math-ph, math.DG, math.FA, math.MP, math.SP]</td>\n",
" <td>None</td>\n",
" </tr>\n",
" <tr>\n",
" <th>38299</th>\n",
" <td>A lower bound for the $Θ$ function on manifolds without conjugate points</td>\n",
" <td>In this short note, we prove that the usual $\\Theta$ function on a Riemannian\\nmanifold without conjugate points is uniformly bounded from below. This extends\\na result of Green in two dimensions. This elementary lemma implies that the\\nB\\'erard remainder in the Weyl law is valid for a manifold without conjugate\\npoints, without any restriction on the dimension.</td>\n",
" <td>1603.05697v1</td>\n",
" <td>[math.DG, math.SP]</td>\n",
" <td>None</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" title \\\n",
"9786 A logarithmic improvement in the two-point Weyl law for manifolds without conjugate points \n",
"39127 Scaling Limit for the Kernel of the Spectral Projector and Remainder Estimates in the Pointwise Weyl Law \n",
"46524 On $L^p$-resolvent estimates and the density of eigenvalues for compact Riemannian manifolds \n",
"38787 C-infinity Scaling Asymptotics for the Spectral Function of the Laplacian \n",
"38299 A lower bound for the $Θ$ function on manifolds without conjugate points \n",
"\n",
" abstract \\\n",
"9786 In this paper, we study the two-point Weyl Law for the Laplace-Beltrami\\noperator on a smooth, compact Riemannian manifold $M$ with no conjugate points.\\nThat is, we find the asymptotic behavior of the Schwartz kernel,\\n$E_\\lambda(x,y)$, of the projection operator from $L^2(M)$ onto the direct sum\\nof eigenspaces with eigenvalue smaller than $\\lambda^2$ as $\\lambda \\to\\infty$.\\nIn the regime where $x,y$ are restricted to a compact neighborhood of the\\ndiagonal in $M\\times M$, we obtain a uniform logarithmic improvement in the\\nremainder of the asymptotic expansion for $E_\\lambda$ and its derivatives of\\nall orders, which generalizes a result of B\\'erard, who treated the on-diagonal\\ncase $E_\\lambda(x,x)$. When $x,y$ avoid a compact neighborhood of the diagonal,\\nwe obtain this same improvement in an upper bound for $E_\\lambda$. Our results\\nimply that the rescaled covariance kernel of a monochromatic random wave\\nlocally converges in the $C^\\infty$ topology to a universal scaling limit at an\\ninverse logarithmic rate. \n",
"39127 Let (M, g) be a compact smooth Riemannian manifold. We obtain new\\noff-diagonal estimates as {\\lambda} tend to infinity for the remainder in the\\npointwise Weyl Law for the kernel of the spectral projector of the Laplacian\\nonto functions with frequency at most {\\lambda}. A corollary is that, when\\nrescaled around a non self-focal point, the kernel of the spectral projector\\nonto the frequency interval (\\lambda, \\lambda + 1] has a universal scaling\\nlimit as {\\lambda} goes to infinity (depending only on the dimension of M). Our\\nresults also imply that if M has no conjugate points, then immersions of M into\\nEuclidean space by an orthonormal basis of eigenfunctions with frequencies in\\n(\\lambda, \\lambda + 1] are embeddings for all {\\lambda} sufficiently large. \n",
"46524 We address an interesting question raised by Dos Santos Ferreira, Kenig and\\nSalo about regions ${\\mathcal R}_g\\subset {\\mathbb C}$ for which there can be\\nuniform $L^{\\frac{2n}{n+2}}\\to L^{\\frac{2n}{n-2}}$ resolvent estimates for\\n$\\Delta_g+\\zeta$, $\\zeta \\in {\\mathcal R}_g$, where $\\Delta_g$ is the\\nLaplace-Beltrami operator with metric $g$ on a given compact boundaryless\\nRiemannian manifold of dimension $n\\ge3$. This is related to earlier work of\\nKenig, Ruiz and the third author for the Euclidean Laplacian, in which case the\\nregion is the entire complex plane minus any disc centered at the origin.\\nPresently, we show that for the round metric on the sphere, $S^n$, the\\nresolvent estimates in Ferreira et al, involving a much smaller region, are\\nessentially optimal. We do this by establishing sharp bounds based on the\\ndistance from $\\zeta$ to the spectrum of $\\Delta_{S^n}$.\\n In the other direction, we also show that the bounds in \\cite{Kenig} can be\\nsharpened logarithmically for manifolds with nonpositive curvature, and by\\npowers in the case of the torus, ${\\mathbb T}^n={\\mathbb R}^n/{\\mathbb Z}^n$,\\nwith the flat metric. The latter improves earlier bounds of Shen.\\n Further improvements for the torus are obtained using recent techniques of\\nthe first author and his work with Guth based on the multilinear estimates of\\nBennett, Carbery and Tao. Our approach also allows us to give a natural\\nnecessary condition for favorable resolvent estimates that is based on a\\nmeasurement of the density of the spectrum of $\\sqrt{-\\Delta_g}$, and,\\nmoreover, a necessary and sufficient condition based on natural improved\\nspectral projection estimates for shrinking intervals. \n",
"38787 This article concerns new off-diagonal estimates on the remainder and its\\nderivatives in the pointwise Weyl law on a compact n-dimensional Riemannian\\nmanifold. As an application, we prove that near any non self-focal point, the\\nscaling limit of the spectral projector of the Laplacian onto frequency windows\\nof constant size is a normalized Bessel function depending only on n. \n",
"38299 In this short note, we prove that the usual $\\Theta$ function on a Riemannian\\nmanifold without conjugate points is uniformly bounded from below. This extends\\na result of Green in two dimensions. This elementary lemma implies that the\\nB\\'erard remainder in the Weyl law is valid for a manifold without conjugate\\npoints, without any restriction on the dimension. \n",
"\n",
" id arxiv_subjects \\\n",
"9786 1905.05136v3 [math.AP, math.SP] \n",
"39127 1411.0658v3 [math.SP, math.AP, math.DG] \n",
"46524 1204.3927v3 [math.AP, math.CA] \n",
"38787 1602.00730v1 [math.AP, math-ph, math.DG, math.FA, math.MP, math.SP] \n",
"38299 1603.05697v1 [math.DG, math.SP] \n",
"\n",
" msc_tags \n",
"9786 [35P20] \n",
"39127 None \n",
"46524 [58J50] \n",
"38787 None \n",
"38299 None "
]
},
"execution_count": 17,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"recs = main(id_list=[\"1905.05136v3\"])\n",
"\n",
"recs.head()"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import pandas as pd\n",
"\n",
"lib = pd.read_feather(\"./data/libraries/APSP_50_allenai-specter/metadata.feather\")"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<style scoped>\n",
" .dataframe tbody tr th:only-of-type {\n",
" vertical-align: middle;\n",
" }\n",
"\n",
" .dataframe tbody tr th {\n",
" vertical-align: top;\n",
" }\n",
"\n",
" .dataframe thead th {\n",
" text-align: right;\n",
" }\n",
"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>title</th>\n",
" <th>abstract</th>\n",
" <th>id</th>\n",
" <th>arxiv_subjects</th>\n",
" <th>msc_tags</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>Post-Lie algebras in Regularity Structures</td>\n",
" <td>In this work, we construct the deformed Butche...</td>\n",
" <td>2208.00514v5</td>\n",
" <td>[math.PR, math.AP, math.RA]</td>\n",
" <td>None</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>Borderline gradient regularity estimates for q...</td>\n",
" <td>In this paper, we study some regularity issues...</td>\n",
" <td>2307.02420v1</td>\n",
" <td>[math.AP]</td>\n",
" <td>None</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>Deep Learning Hydrodynamic Forecasting for Flo...</td>\n",
" <td>Hydrodynamic flood modeling improves hydrologi...</td>\n",
" <td>2305.12052v2</td>\n",
" <td>[cs.LG, math.AP, physics.flu-dyn]</td>\n",
" <td>None</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>Gradient estimates for the non-stationary Stok...</td>\n",
" <td>For the non-stationary Stokes system, it is we...</td>\n",
" <td>2306.16480v2</td>\n",
" <td>[math.AP]</td>\n",
" <td>[35Q30, 35B65]</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>Puiseux asymptotic expansions for convection-d...</td>\n",
" <td>This article completes the study of the influe...</td>\n",
" <td>2307.02387v1</td>\n",
" <td>[math.AP]</td>\n",
" <td>[35K20, 35R02, 35B40, 35B25, 35B45, 35K57, 35Q49]</td>\n",
" </tr>\n",
" <tr>\n",
" <th>...</th>\n",
" <td>...</td>\n",
" <td>...</td>\n",
" <td>...</td>\n",
" <td>...</td>\n",
" <td>...</td>\n",
" </tr>\n",
" <tr>\n",
" <th>49995</th>\n",
" <td>Singular Limits for Thin Film Superconductors ...</td>\n",
" <td>We consider singular limits of the three-dimen...</td>\n",
" <td>1209.3696v1</td>\n",
" <td>[math.AP, math-ph, math.MP]</td>\n",
" <td>[35J50, 35Q56, 49J45]</td>\n",
" </tr>\n",
" <tr>\n",
" <th>49996</th>\n",
" <td>Energy partition for the linear radial wave eq...</td>\n",
" <td>We consider the radial free wave equation in a...</td>\n",
" <td>1209.3678v1</td>\n",
" <td>[math.AP]</td>\n",
" <td>[35L05]</td>\n",
" </tr>\n",
" <tr>\n",
" <th>49997</th>\n",
" <td>Spectral stability for subsonic traveling puls...</td>\n",
" <td>We consider the spectral stability of certain ...</td>\n",
" <td>1209.3666v1</td>\n",
" <td>[math.AP]</td>\n",
" <td>[35B35, 35B40, 35G30]</td>\n",
" </tr>\n",
" <tr>\n",
" <th>49998</th>\n",
" <td>On the extension property of Reifenberg-flat d...</td>\n",
" <td>We provide a detailed proof of the fact that a...</td>\n",
" <td>1209.3602v1</td>\n",
" <td>[math.AP]</td>\n",
" <td>[49Q20, 49Q05, 46E35]</td>\n",
" </tr>\n",
" <tr>\n",
" <th>49999</th>\n",
" <td>BMO estimates for nonvariational operators wit...</td>\n",
" <td>We consider a class of nonvariational linear o...</td>\n",
" <td>1209.3601v1</td>\n",
" <td>[math.AP]</td>\n",
" <td>[35B45]</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"<p>50000 rows × 5 columns</p>\n",
"</div>"
],
"text/plain": [
" title \\\n",
"0 Post-Lie algebras in Regularity Structures \n",
"1 Borderline gradient regularity estimates for q... \n",
"2 Deep Learning Hydrodynamic Forecasting for Flo... \n",
"3 Gradient estimates for the non-stationary Stok... \n",
"4 Puiseux asymptotic expansions for convection-d... \n",
"... ... \n",
"49995 Singular Limits for Thin Film Superconductors ... \n",
"49996 Energy partition for the linear radial wave eq... \n",
"49997 Spectral stability for subsonic traveling puls... \n",
"49998 On the extension property of Reifenberg-flat d... \n",
"49999 BMO estimates for nonvariational operators wit... \n",
"\n",
" abstract id \\\n",
"0 In this work, we construct the deformed Butche... 2208.00514v5 \n",
"1 In this paper, we study some regularity issues... 2307.02420v1 \n",
"2 Hydrodynamic flood modeling improves hydrologi... 2305.12052v2 \n",
"3 For the non-stationary Stokes system, it is we... 2306.16480v2 \n",
"4 This article completes the study of the influe... 2307.02387v1 \n",
"... ... ... \n",
"49995 We consider singular limits of the three-dimen... 1209.3696v1 \n",
"49996 We consider the radial free wave equation in a... 1209.3678v1 \n",
"49997 We consider the spectral stability of certain ... 1209.3666v1 \n",
"49998 We provide a detailed proof of the fact that a... 1209.3602v1 \n",
"49999 We consider a class of nonvariational linear o... 1209.3601v1 \n",
"\n",
" arxiv_subjects \\\n",
"0 [math.PR, math.AP, math.RA] \n",
"1 [math.AP] \n",
"2 [cs.LG, math.AP, physics.flu-dyn] \n",
"3 [math.AP] \n",
"4 [math.AP] \n",
"... ... \n",
"49995 [math.AP, math-ph, math.MP] \n",
"49996 [math.AP] \n",
"49997 [math.AP] \n",
"49998 [math.AP] \n",
"49999 [math.AP] \n",
"\n",
" msc_tags \n",
"0 None \n",
"1 None \n",
"2 None \n",
"3 [35Q30, 35B65] \n",
"4 [35K20, 35R02, 35B40, 35B25, 35B45, 35K57, 35Q49] \n",
"... ... \n",
"49995 [35J50, 35Q56, 49J45] \n",
"49996 [35L05] \n",
"49997 [35B35, 35B40, 35G30] \n",
"49998 [49Q20, 49Q05, 46E35] \n",
"49999 [35B45] \n",
"\n",
"[50000 rows x 5 columns]"
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"lib"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"emb = pd.read_feather(\"./data/libraries/APSP_50_allenai-specter/embeddings.feather\")"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<style scoped>\n",
" .dataframe tbody tr th:only-of-type {\n",
" vertical-align: middle;\n",
" }\n",
"\n",
" .dataframe tbody tr th {\n",
" vertical-align: top;\n",
" }\n",
"\n",
" .dataframe thead th {\n",
" text-align: right;\n",
" }\n",
"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>0</th>\n",
" <th>1</th>\n",
" <th>2</th>\n",
" <th>3</th>\n",
" <th>4</th>\n",
" <th>5</th>\n",
" <th>6</th>\n",
" <th>7</th>\n",
" <th>8</th>\n",
" <th>9</th>\n",
" <th>...</th>\n",
" <th>758</th>\n",
" <th>759</th>\n",
" <th>760</th>\n",
" <th>761</th>\n",
" <th>762</th>\n",
" <th>763</th>\n",
" <th>764</th>\n",
" <th>765</th>\n",
" <th>766</th>\n",
" <th>767</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>-0.354270</td>\n",
" <td>0.422403</td>\n",
" <td>-0.105672</td>\n",
" <td>-0.129077</td>\n",
" <td>0.289177</td>\n",
" <td>0.382220</td>\n",
" <td>0.183098</td>\n",
" <td>0.102091</td>\n",
" <td>0.635695</td>\n",
" <td>1.120547</td>\n",
" <td>...</td>\n",
" <td>0.843546</td>\n",
" <td>-0.591661</td>\n",
" <td>1.413266</td>\n",
" <td>0.980099</td>\n",
" <td>1.254564</td>\n",
" <td>-0.756020</td>\n",
" <td>0.614037</td>\n",
" <td>0.139899</td>\n",
" <td>0.117359</td>\n",
" <td>0.159412</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>-0.005778</td>\n",
" <td>0.875256</td>\n",
" <td>0.844623</td>\n",
" <td>-0.913219</td>\n",
" <td>-0.220542</td>\n",
" <td>0.457574</td>\n",
" <td>0.819090</td>\n",
" <td>0.658583</td>\n",
" <td>-0.206531</td>\n",
" <td>0.899738</td>\n",
" <td>...</td>\n",
" <td>-0.000560</td>\n",
" <td>-0.572531</td>\n",
" <td>0.789380</td>\n",
" <td>1.063664</td>\n",
" <td>-0.072007</td>\n",
" <td>0.111034</td>\n",
" <td>0.270689</td>\n",
" <td>0.319568</td>\n",
" <td>1.085690</td>\n",
" <td>0.670377</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>0.115181</td>\n",
" <td>-0.087180</td>\n",
" <td>0.114065</td>\n",
" <td>0.246189</td>\n",
" <td>0.714248</td>\n",
" <td>0.402952</td>\n",
" <td>0.313888</td>\n",
" <td>0.908008</td>\n",
" <td>0.219879</td>\n",
" <td>1.368971</td>\n",
" <td>...</td>\n",
" <td>0.806028</td>\n",
" <td>-0.331930</td>\n",
" <td>1.068578</td>\n",
" <td>1.111367</td>\n",
" <td>-0.686173</td>\n",
" <td>-0.046650</td>\n",
" <td>-0.116867</td>\n",
" <td>0.380806</td>\n",
" <td>0.239970</td>\n",
" <td>0.928296</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>0.052282</td>\n",
" <td>0.800266</td>\n",
" <td>0.831988</td>\n",
" <td>0.155950</td>\n",
" <td>-0.213863</td>\n",
" <td>0.179749</td>\n",
" <td>1.394324</td>\n",
" <td>0.505120</td>\n",
" <td>-0.341608</td>\n",
" <td>0.040288</td>\n",
" <td>...</td>\n",
" <td>0.333275</td>\n",
" <td>-1.103323</td>\n",
" <td>0.387326</td>\n",
" <td>1.064309</td>\n",
" <td>0.196870</td>\n",
" <td>0.380791</td>\n",
" <td>1.301055</td>\n",
" <td>0.288548</td>\n",
" <td>0.353034</td>\n",
" <td>0.239037</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>0.095074</td>\n",
" <td>0.099750</td>\n",
" <td>0.638213</td>\n",
" <td>-1.026867</td>\n",
" <td>0.020405</td>\n",
" <td>0.488524</td>\n",
" <td>0.555310</td>\n",
" <td>0.269329</td>\n",
" <td>-0.769490</td>\n",
" <td>0.888668</td>\n",
" <td>...</td>\n",
" <td>0.319892</td>\n",
" <td>-0.673623</td>\n",
" <td>0.750743</td>\n",
" <td>0.930013</td>\n",
" <td>0.033606</td>\n",
" <td>0.261526</td>\n",
" <td>0.425253</td>\n",
" <td>0.908287</td>\n",
" <td>1.101179</td>\n",
" <td>0.378441</td>\n",
" </tr>\n",
" <tr>\n",
" <th>...</th>\n",
" <td>...</td>\n",
" <td>...</td>\n",
" <td>...</td>\n",
" <td>...</td>\n",
" <td>...</td>\n",
" <td>...</td>\n",
" <td>...</td>\n",
" <td>...</td>\n",
" <td>...</td>\n",
" <td>...</td>\n",
" <td>...</td>\n",
" <td>...</td>\n",
" <td>...</td>\n",
" <td>...</td>\n",
" <td>...</td>\n",
" <td>...</td>\n",
" <td>...</td>\n",
" <td>...</td>\n",
" <td>...</td>\n",
" <td>...</td>\n",
" <td>...</td>\n",
" </tr>\n",
" <tr>\n",
" <th>49995</th>\n",
" <td>-0.522521</td>\n",
" <td>-0.330984</td>\n",
" <td>0.136525</td>\n",
" <td>-0.450189</td>\n",
" <td>-0.076839</td>\n",
" <td>1.248817</td>\n",
" <td>0.334444</td>\n",
" <td>0.873641</td>\n",
" <td>0.188449</td>\n",
" <td>0.102323</td>\n",
" <td>...</td>\n",
" <td>-0.237047</td>\n",
" <td>-0.376410</td>\n",
" <td>1.547221</td>\n",
" <td>1.126172</td>\n",
" <td>-0.722363</td>\n",
" <td>0.549418</td>\n",
" <td>0.979395</td>\n",
" <td>0.055092</td>\n",
" <td>0.610912</td>\n",
" <td>-0.126857</td>\n",
" </tr>\n",
" <tr>\n",
" <th>49996</th>\n",
" <td>-0.470180</td>\n",
" <td>-0.401946</td>\n",
" <td>0.982030</td>\n",
" <td>-0.207640</td>\n",
" <td>0.532523</td>\n",
" <td>0.231821</td>\n",
" <td>0.380483</td>\n",
" <td>1.066097</td>\n",
" <td>0.130898</td>\n",
" <td>0.458105</td>\n",
" <td>...</td>\n",
" <td>0.178845</td>\n",
" <td>-0.644469</td>\n",
" <td>1.544612</td>\n",
" <td>0.765639</td>\n",
" <td>0.171692</td>\n",
" <td>0.082497</td>\n",
" <td>0.258444</td>\n",
" <td>0.898845</td>\n",
" <td>-0.184204</td>\n",
" <td>-0.039506</td>\n",
" </tr>\n",
" <tr>\n",
" <th>49997</th>\n",
" <td>-1.095224</td>\n",
" <td>0.074697</td>\n",
" <td>0.357558</td>\n",
" <td>-0.289866</td>\n",
" <td>0.776415</td>\n",
" <td>1.029506</td>\n",
" <td>1.334372</td>\n",
" <td>0.711085</td>\n",
" <td>-0.037792</td>\n",
" <td>0.165926</td>\n",
" <td>...</td>\n",
" <td>-0.528522</td>\n",
" <td>-0.889131</td>\n",
" <td>1.200090</td>\n",
" <td>1.039473</td>\n",
" <td>0.167707</td>\n",
" <td>0.511078</td>\n",
" <td>-0.065529</td>\n",
" <td>0.447770</td>\n",
" <td>0.551285</td>\n",
" <td>0.328493</td>\n",
" </tr>\n",
" <tr>\n",
" <th>49998</th>\n",
" <td>-0.344982</td>\n",
" <td>0.121328</td>\n",
" <td>0.305855</td>\n",
" <td>-0.381629</td>\n",
" <td>-0.181680</td>\n",
" <td>0.434278</td>\n",
" <td>1.460984</td>\n",
" <td>0.992868</td>\n",
" <td>0.167097</td>\n",
" <td>1.005540</td>\n",
" <td>...</td>\n",
" <td>0.580155</td>\n",
" <td>-0.436302</td>\n",
" <td>0.818202</td>\n",
" <td>0.528767</td>\n",
" <td>0.078137</td>\n",
" <td>0.811233</td>\n",
" <td>0.269796</td>\n",
" <td>0.241384</td>\n",
" <td>-0.356777</td>\n",
" <td>0.245386</td>\n",
" </tr>\n",
" <tr>\n",
" <th>49999</th>\n",
" <td>-0.758263</td>\n",
" <td>0.188403</td>\n",
" <td>0.582321</td>\n",
" <td>-1.106614</td>\n",
" <td>0.063970</td>\n",
" <td>0.288577</td>\n",
" <td>0.510509</td>\n",
" <td>0.543814</td>\n",
" <td>-0.262185</td>\n",
" <td>0.727537</td>\n",
" <td>...</td>\n",
" <td>0.017372</td>\n",
" <td>-0.628980</td>\n",
" <td>1.412982</td>\n",
" <td>1.034429</td>\n",
" <td>0.289884</td>\n",
" <td>-0.282774</td>\n",
" <td>0.831488</td>\n",
" <td>0.248558</td>\n",
" <td>0.771177</td>\n",
" <td>-0.124385</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"<p>50000 rows × 768 columns</p>\n",
"</div>"
],
"text/plain": [
" 0 1 2 3 4 5 6 \\\n",
"0 -0.354270 0.422403 -0.105672 -0.129077 0.289177 0.382220 0.183098 \n",
"1 -0.005778 0.875256 0.844623 -0.913219 -0.220542 0.457574 0.819090 \n",
"2 0.115181 -0.087180 0.114065 0.246189 0.714248 0.402952 0.313888 \n",
"3 0.052282 0.800266 0.831988 0.155950 -0.213863 0.179749 1.394324 \n",
"4 0.095074 0.099750 0.638213 -1.026867 0.020405 0.488524 0.555310 \n",
"... ... ... ... ... ... ... ... \n",
"49995 -0.522521 -0.330984 0.136525 -0.450189 -0.076839 1.248817 0.334444 \n",
"49996 -0.470180 -0.401946 0.982030 -0.207640 0.532523 0.231821 0.380483 \n",
"49997 -1.095224 0.074697 0.357558 -0.289866 0.776415 1.029506 1.334372 \n",
"49998 -0.344982 0.121328 0.305855 -0.381629 -0.181680 0.434278 1.460984 \n",
"49999 -0.758263 0.188403 0.582321 -1.106614 0.063970 0.288577 0.510509 \n",
"\n",
" 7 8 9 ... 758 759 760 \\\n",
"0 0.102091 0.635695 1.120547 ... 0.843546 -0.591661 1.413266 \n",
"1 0.658583 -0.206531 0.899738 ... -0.000560 -0.572531 0.789380 \n",
"2 0.908008 0.219879 1.368971 ... 0.806028 -0.331930 1.068578 \n",
"3 0.505120 -0.341608 0.040288 ... 0.333275 -1.103323 0.387326 \n",
"4 0.269329 -0.769490 0.888668 ... 0.319892 -0.673623 0.750743 \n",
"... ... ... ... ... ... ... ... \n",
"49995 0.873641 0.188449 0.102323 ... -0.237047 -0.376410 1.547221 \n",
"49996 1.066097 0.130898 0.458105 ... 0.178845 -0.644469 1.544612 \n",
"49997 0.711085 -0.037792 0.165926 ... -0.528522 -0.889131 1.200090 \n",
"49998 0.992868 0.167097 1.005540 ... 0.580155 -0.436302 0.818202 \n",
"49999 0.543814 -0.262185 0.727537 ... 0.017372 -0.628980 1.412982 \n",
"\n",
" 761 762 763 764 765 766 767 \n",
"0 0.980099 1.254564 -0.756020 0.614037 0.139899 0.117359 0.159412 \n",
"1 1.063664 -0.072007 0.111034 0.270689 0.319568 1.085690 0.670377 \n",
"2 1.111367 -0.686173 -0.046650 -0.116867 0.380806 0.239970 0.928296 \n",
"3 1.064309 0.196870 0.380791 1.301055 0.288548 0.353034 0.239037 \n",
"4 0.930013 0.033606 0.261526 0.425253 0.908287 1.101179 0.378441 \n",
"... ... ... ... ... ... ... ... \n",
"49995 1.126172 -0.722363 0.549418 0.979395 0.055092 0.610912 -0.126857 \n",
"49996 0.765639 0.171692 0.082497 0.258444 0.898845 -0.184204 -0.039506 \n",
"49997 1.039473 0.167707 0.511078 -0.065529 0.447770 0.551285 0.328493 \n",
"49998 0.528767 0.078137 0.811233 0.269796 0.241384 -0.356777 0.245386 \n",
"49999 1.034429 0.289884 -0.282774 0.831488 0.248558 0.771177 -0.124385 \n",
"\n",
"[50000 rows x 768 columns]"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"emb"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.11.4"
},
"orig_nbformat": 4
},
"nbformat": 4,
"nbformat_minor": 2
}
|