{ "cells": [ { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ "import importlib" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [], "source": [ "import pandas as pd\n", "\n", "pd.set_option(\"display.max_colwidth\", 0)" ] }, { "cell_type": "code", "execution_count": 47, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 47, "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": 39, "metadata": {}, "outputs": [], "source": [ "## Load library\n", "library_path = \"./data/APSP_50.feather\"\n", "path_to_library_embeddings = \"./data/allenai-specter_APSP_50_embeddings.feather\"\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": [ "
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titleabstractidarxiv_subjectsmsc_tagsdoc_strings
38787C-infinity Scaling Asymptotics for the Spectral Function of the LaplacianThis 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.1602.00730v1[math.AP, math-ph, math.DG, math.FA, math.MP, math.SP]NoneC-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.
39127Scaling Limit for the Kernel of the Spectral Projector and Remainder Estimates in the Pointwise Weyl LawLet (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.1411.0658v3[math.SP, math.AP, math.DG]NoneScaling 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.
9786A logarithmic improvement in the two-point Weyl law for manifolds without conjugate pointsIn 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.1905.05136v3[math.AP, math.SP][Asymptotic distributions of eigenvalues in context of PDEs]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.
49609The blowup along the diagonal of the spectral function of the LaplacianWe 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.1103.1276v4[math.DG, math-ph, math.AP, math.MP][Spectral problems; spectral geometry; scattering theory on manifolds, Second-order elliptic equations]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.
14857Growth of high LATEX norms for eigenfunctions: an application of geodesic beamsThis 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 LATEX2003.04597v2[math.AP, math.SP]NoneGrowth 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
\n", "
" ], "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": 20, "metadata": {}, "outputs": [], "source": [ "id_list = [\"1602.00730\"]" ] }, { "cell_type": "code", "execution_count": 46, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 46, "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": 47, "metadata": {}, "outputs": [], "source": [ "## Fetch metadata of input\n", "getter = Fetch()\n", "into_cleaner = getter.transform(X=id_list)" ] }, { "cell_type": "code", "execution_count": 48, "metadata": {}, "outputs": [], "source": [ "cleaner = TextCleaner()\n", "\n", "into_embedder = cleaner.transform(into_cleaner)" ] }, { "cell_type": "code", "execution_count": 49, "metadata": {}, "outputs": [], "source": [ "embedder = Embedder(model_name=\"allenai-specter\")\n", "into_search = embedder.transform(into_embedder)" ] }, { "cell_type": "code", "execution_count": 52, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "['1602.00730v1', '1411.0658v3', '1905.05136v3', '1103.1276v4', '2003.04597v2']" ] }, "execution_count": 52, "metadata": {}, "output_type": "execute_result" } ], "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": 54, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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titleabstractidarxiv_subjectsmsc_tags
38787C-infinity Scaling Asymptotics for the Spectra...This article concerns new off-diagonal estimat...1602.00730v1[math.AP, math-ph, math.DG, math.FA, math.MP, ...None
39127Scaling Limit for the Kernel of the Spectral P...Let (M, g) be a compact smooth Riemannian mani...1411.0658v3[math.SP, math.AP, math.DG]None
9786A logarithmic improvement in the two-point Wey...In this paper, we study the two-point Weyl Law...1905.05136v3[math.AP, math.SP][35P20]
49609The blowup along the diagonal of the spectral ...We formulate a precise conjecture about the un...1103.1276v4[math.DG, math-ph, math.AP, math.MP][58J50, 35J15, 33C45, 32C05]
14857Growth of high $L^p$ norms for eigenfunctions:...This work concerns $L^p$ norms of high energy ...2003.04597v2[math.AP, math.SP]None
\n", "
" ], "text/plain": [ " title ... msc_tags\n", "38787 C-infinity Scaling Asymptotics for the Spectra... ... None\n", "39127 Scaling Limit for the Kernel of the Spectral P... ... None\n", "9786 A logarithmic improvement in the two-point Wey... ... [35P20]\n", "49609 The blowup along the diagonal of the spectral ... ... [58J50, 35J15, 33C45, 32C05]\n", "14857 Growth of high $L^p$ norms for eigenfunctions:... ... None\n", "\n", "[5 rows x 5 columns]" ] }, "execution_count": 54, "metadata": {}, "output_type": "execute_result" } ], "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)" ] } ], "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": "3.10.11" }, "orig_nbformat": 4 }, "nbformat": 4, "nbformat_minor": 2 }