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arXiv 2023年

作者： Akiyama, Kazunori Alberdi, Antxon Alef, Walter Algaba, Juan Carlos Anantua, Richard Asada, Keiichi Azulay, Rebecca Bach, Uwe Baczko, Anne-Kathrin Ball, David Baloković, Mislav Bandyopadhyay, Bidisha Barrett, John Bauböck, Michi Benson, Bradford A. Bintley, Dan Blackburn, Lindy Blundell, Raymond Bouman, Katherine L. Bower, Geoffrey C. Boyce, Hope Bremer, Michael Brinkerink, Christiaan D. Brissenden, Roger Britzen, Silke Broderick, Avery E. Broguiere, Dominique Bronzwaer, Thomas Bustamante, Sandra Byun, Do-Young Carlstrom, John E. Ceccobello, Chiara Chael, Andrew Chan, Chi-Kwan Chang, Dominic O. Chatterjee, Koushik Chatterjee, Shami Chen, Ming-Tang Chen, Yongjun Cheng, Xiaopeng Cho, Ilje Christian, Pierre Conroy, Nicholas S. Conway, John E. Cordes, James M. Crawford, Thomas M. Crew, Geoffrey B. Cruz-Osorio, Alejandro Cui, Yuzhu Dahale, Rohan Davelaar, Jordy De Laurentis, Mariafelicia Deane, Roger Dempsey, Jessica Desvignes, Gregory Dexter, Jason Dhruv, Vedant Dihingia, Indu K. Doeleman, Sheperd S. Dougal, Sean Dzib, Sergio A. Eatough, Ralph P. Emami, Razieh Falcke, Heino Farah, Joseph Fish, Vincent L. Fomalont, Ed Ford, H. Alyson Foschi, Marianna Fraga-Encinas, Raquel Freeman, William T. Friberg, Per Fromm, Christian M. Fuentes, Antonio Galison, Peter Gammie, Charles F. García, Roberto Gentaz, Olivier Georgiev, Boris Goddi, Ciriaco Gold, Roman Gómez-Ruiz, Arturo I. Gómez, José L. Gu, Minfeng Gurwell, Mark Hada, Kazuhiro Haggard, Daryl Haworth, Kari Hecht, Michael H. Hesper, Ronald Heumann, Dirk Ho, Luis C. Ho, Paul Honma, Mareki Huang, Chih-Wei L. Huang, Lei Hughes, David H. Ikeda, Shiro Impellizzeri, C.M. Violette Inoue, Makoto Issaoun, Sara James, David J. Jannuzi, Buell T. Janssen, Michael Jeter, Britton Jiang, Wu Jiménez-Rosales, Alejandra Johnson, Michael D. Jorstad, Svetlana Joshi, Abhishek V. Jung, Taehyun Karami, Mansour Karuppusamy, Ramesh Kawashima, Tomohisa Keating, Garrett K. Kettenis, Mark Kim, Dong-Jin Kim, Jae-Young Kim, Jongsoo Kim, Junhan Kino, Motoki Koay, Jun Yi Kocherlakota, Prashant Kofuji, Yut Massachusetts Institute of Technology Haystack Observatory 99 Millstone Road WestfordMA01886 United States National Astronomical Observatory of Japan 2-21-1 Osawa Mitaka Tokyo181-8588 Japan Black Hole Initiative Harvard University 20 Garden Street CambridgeMA02138 United States Instituto de Astrofísica de Andalucía-CSIC Glorieta de la Astronomía s/n GranadaE-18008 Spain Max-Planck-Institut für Radioastronomie Auf dem Hügel 69 BonnD-53121 Germany Department of Physics Faculty of Science Universiti Malaya Kuala Lumpur50603 Malaysia Center for Astrophysics Harvard & Smithsonian 60 Garden Street CambridgeMA02138 United States Department of Physics & Astronomy The University of Texas at San Antonio One UTSA Circle San AntonioTX78249 United States Institute of Astronomy and Astrophysics Academia Sinica 11F of Astronomy-Mathematics Building AS/NTU No. 1 Sec. 4 Roosevelt Rd. Taipei10617 Taiwan Departament d’Astronomia i Astrofísica Universitat de València C. Dr. Moliner 50 Burjassot ValènciaE-46100 Spain Observatori Astronòmic Universitat de València C. Catedrático José Beltrán 2 Paterna ValènciaE-46980 Spain Department of Space Earth and Environment Chalmers University of Technology Onsala Space Observatory OnsalaSE-43992 Sweden Steward Observatory Department of Astronomy University of Arizona 933 N. Cherry Ave. TucsonAZ85721 United States Yale Center for Astronomy & Astrophysics Yale University 52 Hillhouse Avenue New HavenCT06511 United States Astronomy Department Universidad de Concepción Casilla 160-C Concepción Chile Department of Physics University of Illinois 1110 West Green Street UrbanaIL61801 United States Fermi National Accelerator Laboratory MS209 P.O. Box 500 BataviaIL60510 United States Department of Astronomy and Astrophysics University of Chicago 5640 South Ellis Avenue ChicagoIL60637 United States East Asian Observatory 660 N. A’ohoku Place HiloHI96720 United States 660 N. A’ohoku Place HiloHI

Event Horizon Telescope (EHT) observations have revealed a bright ring of emission around the supermassive black hole at the center of the M87 galaxy. EHT images in linear polarization have further identified a coherent spiral pattern around the black hole, produced from ordered magnetic fields threading the emitting plasma. Here, we present the first analysis of circular polarization using EHT data, acquired in 2017, which can potentially provide additional insights into the magnetic fields and plasma composition near the black hole. Interferometric closure quantities provide convincing evidence for the presence of circularly polarized emission on event-horizon scales. We produce images of the circular polarization using both traditional and newly developed methods. All methods find a moderate level of resolved circular polarization across the image (〈|v|〉 int| ∗ © 2023, CC BY.

关键词： Circular polarization

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Numerical equivalence between sph and probabilistic mass transfer methods for lagrangian simulation of dispersioni

arXiv

引用

arXiv 2018年

作者： Sole-Mari, Guillem Schmidt, Michael J. Pankavich, Stephen D. Benson, David A. Universitat Politècnica de Catalunya Barcelona Spain UPC-CSIC Barcelona Spain Department of Applied Mathematics and Statistics Colorado School of Mines GoldenCO80401 United States Hydrologic Science and Engineering Program Department of Geology and Geological Engineering Colorado School of Mines GoldenCO80401 United States

Several Lagrangian methodologies have been proposed in recent years to simulate advection-dispersion of solutes in fluids as a mass exchange between numerical particles carrying the fluid. In this paper, we unify these methodologies, showing that mass transfer particle tracking (MTPT) algorithms can be framed within the context of smoothed particle hydrodynamics (SPH), provided the choice of a Gaussian smoothing kernel whose bandwidth depends on the dispersion and the time discretization. Numerical simulations are performed for a simple dispersion problem, and they are compared to an analytical solution. Based on the results, we advocate for the use of a kernel bandwidth of the size of the characteristic dispersion length ` = √2D∆t, at least given a "dense enough" distribution of particles, for in this case the mass transfer operation is not just an approximation, but in fact the exact solution, of the solute’s displacement Copyright © 2018, The Authors. All rights reserved.

关键词： Mass transfer

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Nonbacktracking bounds on the influence in independent cascade models

arXiv

引用

arXiv 2017年

作者： Abbe, Emmanuel Kulkarni, Sanjeev Lee, Eun Jee Program in Applied and Computational Mathematics Department of Electrical Engineering Princeton University Princeton United States Department of Electrical Engineering Princeton University Princeton United States Program in Applied and Computational Mathematics Princeton University Princeton United States

This paper develops upper and lower bounds on the influence measure in a network, more precisely, the expected number of nodes that a seed set can influence in the independent cascade model. In particular, our bounds exploit nonbacktracking walks, Fortuin–Kasteleyn–Ginibre (FKG) type inequalities, and are computed by message passing implementation. Nonbacktracking walks have recently allowed for headways in community detection, and this paper shows that their use can also impact the influence computation. Further, we provide a knob to control the trade-off between the efficiency and the accuracy of the bounds. Finally, the tightness of the bounds is illustrated with simulations on various network models. Copyright © 2017, The Authors. All rights reserved.

关键词： Economic and social effects

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Rethinking CO antibiosignatures in the search for life beyond the solar system

arXiv

引用

arXiv 2019年

作者： Schwieterman, Edward W. Reinhard, Christopher T. Olson, Stephanie L. Ozaki, Kazumi Harman, Chester E. Hong, Peng K. Lyons, Timothy W. Department of Earth Sciences University of California RiversideCA United States NASA Postdoctoral Program Universities Space Research Association ColumbiaMD United States NASA Astrobiology Institute Alternative Earths & Virtual Planetary Laboratory Teams United States Blue Marble Space Institute of Science SeattleWA United States School of Earth and Atmospheric Sciences Georgia Institute of Technology AtlantaGA United States Department of Geophysical Sciences University of Chicago ChicagoIL United States Department of Environmental Science Toho University Tokyo Japan NASA Goddard Institute for Space Studies New YorkNY United States Department of Applied Mathematics and Applied Physics Columbia University New YorkNY United States Planetary Exploration Research Center Chiba Institute of Technology 2-17-1 Tsudanuma Narashino Chiba275-0016 Japan

Some atmospheric gases have been proposed as counter indicators to the presence of life on an exoplanet if remotely detectable at sufficient abundance (i.e., antibiosignatures), informing the search for biosignatures and potentially fingerprinting uninhabited habitats. However, the quantitative extent to which putative antibiosignatures could exist in the atmospheres of inhabited planets is not well understood. The most commonly referenced potential antibiosignature is CO, because it represents a source of free energy and reduced carbon that is readily exploited by life on Earth and is thus often assumed to accumulate only in the absence of life. Yet, biospheres actively produce CO through biomass burning, photooxidation processes, and release of gases that are photochemically converted into CO in the atmosphere. We demonstrate with a 1D ecosphere-atmosphere model that reducing biospheres can maintain CO levels of ~100 ppmv even at low H2fluxes due to the impact of hybrid photosynthetic ecosystems. Additionally, we show that photochemistry around M dwarf stars is particularly favorable for the buildup of CO, with plausible concentrations for inhabited, oxygen-rich planets extending from hundreds of ppm to several percent. Since CH4buildup is also favored on these worlds, and because O2and O3are likely not detectable with the James Webb Space Telescope, the presence of high CO (>100 ppmv) may discriminate between oxygen-rich and reducing biospheres with near-future transmission observations. These results suggest that spectroscopic detection of CO can be compatible with the presence of life and that a comprehensive contextual assessment is required to validate the significance of potential antibiosignatures. Copyright © 2019, The Authors. All rights reserved.

关键词： Free energy

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Author Correction: Comprehensive molecular characterization of mitochondrial genomes in human cancers

引用

Nature genetics 2023年第6期55卷 1078页

作者： Yuan Yuan Young Seok Ju Youngwook Kim Jun Li Yumeng Wang Christopher J Yoon Yang Yang Inigo Martincorena Chad J Creighton John N Weinstein Yanxun Xu Leng Han Hyung-Lae Kim Hidewaki Nakagawa Keunchil Park Peter J Campbell Han Liang Department of Bioinformatics and Computational Biology The University of Texas MD Anderson Cancer Center Houston TX USA. Cancer Genome Project Wellcome Trust Sanger Institute Hinxton UK. Graduate School of Medical Science and Engineering Korea Advanced Institute of Science and Technology Daejeon Korea. Department of Health Science and Technology Samsung Advanced Institute for Health Science and Technology Sungkyunkwan University School of Medicine Seoul Korea. Samsung Genome Institute Samsung Medical Center Seoul Korea. Quantitative and Computational Biosciences Graduate Program Baylor College of Medicine Houston TX USA. Division of Biostatistics The University of Texas Health Science Center at Houston School of Public Health Houston TX USA. Department of Medicine and Dan L. Duncan Cancer Center Division of Biostatistics Baylor College of Medicine Houston TX USA. Department of Systems Biology The University of Texas MD Anderson Cancer Center Houston TX USA. Department of Applied Mathematics and Statistics Johns Hopkins University Baltimore MD USA. Department of Biochemistry and Molecular Biology The University of Texas Health Science Center at Houston McGovern Medical School Houston TX USA. Department of Biochemistry Ewha Womans University School of Medicine Seoul Korea. Laboratory for Cancer Genomics RIKEN Center for Integrative Medical Sciences Yokohama Japan. Division of Hematology/Oncology Samsung Medical Center Sungkyunkwan University School of Medicine Seoul Korea. kpark@skku.edu. Samsung Advanced Institute for Health Sciences and Technology Sungkyunkwan University School of Medicine Seoul South Korea. kpark@skku.edu. Cancer Genome Project Wellcome Trust Sanger Institute Hinxton UK. pc8@sanger.ac.uk. Department of Haematology University of Cambridge Cambridge UK. pc8@sanger.ac.uk. Department of Bioinformatics and Computational Biology The University of Texas MD Anderson Cancer Center Houston TX USA. hliang1@mdanderson.org. Quantitative and Comp

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Efficient algorithms for T-distributed stochastic neighborhood embedding

arXiv

引用

arXiv 2017年

作者： Linderman, George C. Rachh, Manas Hoskins, Jeremy G. Steinerberger, Stefan Kluger, Yuval Applied Mathematics Program Yale University New HavenCT06511 United States Department of Mathematics Yale University New HavenCT06511 United States Department of Pathology and Applied Mathematics Program Yale University School of Medicine New HavenCT06511 United States

t-distributed Stochastic Neighborhood Embedding (t-SNE) is a method for dimensionality reduction and visualization that has become widely popular in recent years. Efficient implementations of t-SNE are available, but they scale poorly to datasets with hundreds of thousands to millions of high dimensional data-points. We present Fast Fourier Transform-accelerated Interpolation-based t-SNE (FIt-SNE), which dramatically accelerates the computation of t-SNE. The most time-consuming step of t-SNE is a convolution that we accelerate by interpolating onto an equispaced grid and subsequently using the fast Fourier transform to perform the convolution. We also optimize the computation of input similarities in high dimensions using multi-threaded approximate nearest neighbors. We further present a modification to t-SNE called "late exaggeration," which allows for easier identification of clusters in t-SNE embeddings. Finally, for datasets that cannot be loaded into the memory, we present out-of-core randomized principal component analysis (oocPCA), so that the top principal components of a dataset can be computed without ever fully loading the matrix, hence allowing for t-SNE of large datasets to be computed on resource-limited machines. Copyright © 2017, The Authors. All rights reserved.

关键词： Stochastic systems

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Light Localization in Local Isomorphism Classes of Quasicrystals

引用

Physical Review Letters 2018年第24期120卷 247401-247401页

作者： Chaney Lin Paul J. Steinhardt Salvatore Torquato Department of Physics Princeton University Princeton New Jersey 08544 USA Princeton Center for Theoretical Science Princeton University Princeton New Jersey 08544 USA Department of Chemistry Princeton University Princeton New Jersey 08544 USA Program of Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA Princeton Institute for the Science and Technology of Materials Princeton University Princeton New Jersey 08544 USA

We study a continuum of photonic quasicrystal heterostructures derived from local isomorphism (LI) classes of pentagonal quasicrystal tilings. These tilings are obtained by direct projection from a five-dimensional hypercubic lattice. We demonstrate that, with the sole exception of the Penrose LI class, all other LI classes result in degenerate, effectively localized states, with precisely predictable and tunable properties (frequencies, frequency splittings, and densities). We show that localization and tunability are related to a mathematical property of the pattern known as “restorability,” i.e., whether the tiling can be uniquely specified given only a set of rules that fix all allowed clusters smaller than some bound.

关键词： Photonic crystals Photonics Quasicrystals

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Scattering of a short electromagnetic pulse from a Lorentz-Duffing film: Theoretical and numerical analysis

arXiv

引用

arXiv 2018年

作者： Brio, Moysey Caputo, Jean-Guy Gwirtz, Kyle Liu, Jinjie Maimistov, Andrei Department of Mathematics University of Arizona TucsonAZ85721 United States Laboratoire de Mathématiques INSA Rouen Normandie Saint-Etienne du Rouvray76801 France Program in Applied Mathematics University of Arizona TucsonAZ85721 United States Department of Mathematical Sciences Delaware State University DoverDE19901 United States Department of Solid State Physics and Nanostructures National Research Nuclear University Moscow Engineering Physics Institute Kashirskoe sh. 31 Moscow115409 Russia

We combine scattering theory, Fourier, traveling wave and asymptotic analyses together with numerical simulations to present interesting and practically useful properties of femtosecond pulse interaction with thin films. The dispersive material is described by a single resonance Lorentz model and its nonlinear extension with a cubic Duffing-type nonlinearity. A key feature of the Lorentz dielectric function is that its real part becomes negative between its zero and its pole, generating a forbidden region. We illustrate numerically the linear interaction of the pulse with the film using both scattering theory and Fourier analysis. Outside this region we show the generation of a sequence of pulses separated by round trips in the Fabry-Perot cavity due to multiple reflections. When the pulse spectrum is inside the forbidden region, we observe total reflection. Near the pole of the dielectric function, we demonstrate the slowing down of the pulse (group velocity tending to zero) in the medium that behaves as a high-Q cavity. We use the combination of analysis and simulations in the linear regime to validate the delta function approximation of the thin layer;this collapses the forbidden region to a single resonant point of the spectrum. We also study the single cycle pulse interaction with a thin film and show three distinct types of reflection: half-pulse, sinusoidal wave train and cosine wavelet. Finally we analyze the influence of a strong nonlinearity and observe that the film switches from reflecting to trasparent. Copyright © 2018, The Authors. All rights reserved.

关键词： Thin films

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Input optics systems of the KAGRA detector during O3GK (vol 2023, 023F01, 2023)

引用

PROGRESS OF THEORETICAL AND EXPERIMENTAL PHYSICS 2023年第5期2023卷

作者： Akutsu, T. Ando, M. Arai, K. Arai, Y. Araki, S. Araya, A. Aritomi, N. Asada, H. Aso, Y. Bae, S. Bae, Y. Baiotti, L. Bajpai, R. Barton, M. A. Cannon, K. Cao, Z. Capocasa, E. Chan, M. Chen, C. Chen, K. Chen, Y. Chiang, C-I Chu, H. Chu, Y-K Eguchi, S. Enomoto, Y. Flaminio, R. Fujii, Y. Fujikawa, Y. Fukunaga, M. Fukushima, M. Furuhata, T. Gao, D. Ge, G-G Ha, S. Hagiwara, A. Haino, S. Han, W-B Hasegawa, K. Hattori, K. Hayakawa, H. Hayama, K. Himemoto, Y. Hiranuma, Y. Hirata, N. Hirose, E. Hong, Z. Hsieh, B-H Huang, G-Z Huang, H-Y Huang, P. Huang, Y-C Huang, Y-J Hui, D. C. Y. Ide, S. Ikenoue, B. Imam, S. Inayoshi, K. Inoue, Y. Ioka, K. Ito, K. Itoh, Y. Izumi, K. Jeon, C. Jin, H-B Jung, K. Jung, P. Kaihotsu, K. Kajita, T. Kakizaki, M. Kamiizumi, M. Kanbara, S. Kanda, N. Kang, G. Kataoka, Y. Kawaguchi, K. Kawai, N. Kawasaki, T. Kim, C. Kim, J. Kim, J. C. Kim, Ws Kim, Y-M Kimura, N. Kita, N. Kitazawa, H. Kojima, Y. Kokeyama, K. Komori, K. Kong, A. K. H. Kotake, K. Kozakai, C. Kozu, R. Kumar, R. Kume, J. Kuo, C. Kuo, H-S Kuromiya, Y. Kuroyanagi, S. Kusayanagi, K. Kwak, K. Lee, H. K. Lee, H. W. Lee, R. Leonardi, M. Li, K. L. Lin, L. C-C Lin, C-Y Lin, F-K Lin, F-L Lin, H. L. Liu, G. C. Luo, L-W Majorana, E. Marchio, M. Michimura, Y. Mio, N. Miyakawa, O. Miyamoto, A. Miyazaki, Y. Miyo, K. Miyoki, S. Mori, Y. Morisaki, S. Moriwaki, Y. Nagano, K. Nagano, S. Nakamura, K. Nakano, H. Nakano, M. Nakashima, R. Nakayama, Y. Narikawa, T. Naticchioni, L. Negishi, R. Quynh, L. Nguyen Ni, W-T Nishizawa, A. Nozaki, S. Obuchi, Y. Ogaki, W. Oh, J. J. Oh, S. H. Ohashi, M. Ohishi, N. Ohkawa, M. Ohta, H. Okutani, Y. Okutomi, K. Oohara, K. Ooi, C. Oshino, S. Otabe, S. Pan, K-C Pang, H. Parisi, A. Park, J. Arellano, F. E. Pena Pinto, I. Sago, N. Saito, S. Saito, Y. Sakai, K. Sakai, Y. Sakuno, Y. Sato, S. Sato, T. Sawada, T. Sekiguchi, T. Sekiguchi, Y. Shao, L. Shibagaki, S. Shimizu, R. Shimoda, T. Shimode, K. Shinkai, H. Shishido, T. Shoda, A. Somiya, K. Son, E. J. Sotani, H. Sugimoto, R. Suresh, J. Suzuki, T. Suzuki, T. Tagoshi, H. Takahashi, H Gravitational Wave Science Project National Astronomical Observatory of Japan 2-21-1 Osawa Mitaka City Tokyo 181-8588 Japan Advanced Technology Center National Astronomical Observatory of Japan 2-21-1 Osawa Mitaka City Tokyo 181-8588 Japan Department of Physics The University of Tokyo 7-3-1 Hongo Bunkyo-ku Tokyo 113-0033 Japan Research Center for the Early Universe The University of Tokyo 7-3-1 Hongo Bunkyo-ku Tokyo 113-0033 Japan Institute for Cosmic Ray Research KAGRA Observatory The University of Tokyo 5-1-5 Kashiwa-no-Ha Kashiwa City Chiba 277-8582 Japan Accelerator Laboratory High Energy Accelerator Research Organization (KEK) 1-1 Oho Tsukuba City Ibaraki 305-0801 Japan Earthquake Research Institute The University of Tokyo 1-1-1 Yayoi Bunkyo-ku Tokyo 113-0032 Japan Department of Mathematics and Physics Graduate School of Science and Technology Hirosaki University 3 Bunkyo-cho Hirosaki Aomori 036-8561 Japan Kamioka Branch National Astronomical Observatory of Japan 238 Higashi-Mozumi Kamioka-cho Hida City Gifu 506-1205 Japan The Graduate University for Advanced Studies (SOKENDAI) 2-21-1 Osawa Mitaka City Tokyo 181-8588 Japan Korea Institute of Science and Technology Information 245 Daehak-ro Yuseong-gu Daejeon 34141 Republic of Korea National Institute for Mathematical Sciences 70 Yuseong-daero 1689 Beon-gil Yuseong-gu Daejeon 34047 Republic of Korea International College Osaka University 1-1 Machikaneyama-cho Toyonaka City Osaka 560-0043 Japan School of High Energy Accelerator Science The Graduate University for Advanced Studies (SOKENDAI) 1-1 Oho Tsukuba City Ibaraki 305-0801 Japan Department of Astronomy Beijing Normal University Xinjiekouwai Street 19 Haidian District Beijing 100875 China Department of Applied Physics Fukuoka University 8-19-1 Nanakuma Jonan Fukuoka City Fukuoka 814-0180 Japan Department of Physics Tamkang University No. 151 Yingzhuan Road Danshui Dist. New Taipei City 25137 Taiwan Department of Physics

KAGRA, the underground and cryogenic gravitational-wave detector, was operated for its solo observation from February 25 to March 10, 2020, and its first joint observation with the GEO 600 detector from April 7 to April 21, 2020 (O3GK). This study presents an overview of the input optics systems of the KAGRA detector, which consist of various optical systems, such as a laser source, its intensity and frequency stabilization systems, modulators, a Faraday isolator, mode-matching telescopes, and a high-power beam dump. These optics were successfully delivered to the KAGRA interferometer and operated stably during the observations. The laser frequency noise was observed to limit the detector sensitivity above a few kilohertz, whereas the laser intensity did not significantly limit the detector sensitivity.

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Quantifying Gerrymandering in North Carolina

arXiv

引用

arXiv 2018年

作者： Herschlag, Gregory Kang, Han Sung Luo, Justin Graves, Christy Vaughn Bangia, Sachet Ravier, Robert Mattingly, Jonathan C. Department of Mathematics Duke University DurhamNC27708 United States Department of Biomedical Engineering Duke University DurhamNC27708 United States Department of Computer Science Duke University DurhamNC27708 United States Department of Electrical and Computer Engineering Duke University DurhamNC27708 United States Department of Economics Duke University DurhamNC27708 United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ United States Department of Statistical Science Duke University DurhamNC27708 United States

Using an ensemble of redistricting plans, we evaluate whether a given political districting faithfully represents the geo-political landscape. Redistricting plans are sampled by a Monte Carlo algorithm from a probability distribution that adheres to realistic and non-partisan criteria. Using the sampled redistricting plans and historical voting data, we produce an ensemble of elections that reveal geo-political structure within the state. We showcase our methods on the two most recent districtings of NC for the U.S. House of Representatives, as well as a plan drawn by a bipartisan redistricting panel. We find the two state enacted plans are highly atypical outliers whereas the bipartisan plan accurately represents the ensemble both in partisan outcome and in the fine scale structure of district-level results. Copyright © 2018, The Authors. All rights reserved.

关键词： Probability distributions

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