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The Simons Observatory: Constraining inationary gravitational waves with multi-tracer B-mode delensing

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arXiv 2021年

作者： Namikawa, Toshiya Lizancos, Anton Baleato Robertson, Naomi Sherwin, Blake D. Challinor, Anthony Alonso, David Azzoni, Susanna Baccigalupi, Carlo Calabrese, Erminia Carron, Julien Chinone, Yuji Chluba, Jens Coppi, Gabriele Errard, Josquin Fabbian, Giulio Ferraro, Simone Kalaja, Alba Lewis, Antony Madhavacheril, Mathew S. Meerburg, P. Daniel Meyers, Joel Nati, Federico Orlando, Giorgio Poletti, Davide Puglisi, Giuseppe Remazeilles, Mathieu Sehgal, Neelima Tajima, Osamu Teply, Grant Van Engelen, Alexander Wollack, Edward J. Xu, Zhilei Yu, Byeonghee Zhu, Ningfeng Zonca, Andrea Utias The University of Tokyo Chiba Kashiwa277-8583 Japan Department of Applied Mathematics and Theoretical Physics University of Cambridge Wilberforce Road CambridgeCB3 0WA United Kingdom Institute of Astronomy Madingley Road CambridgeCB3 0HA United Kingdom Kavli Institute for Cosmology Cambridge Madingley Road CambridgeCB3 0HA United Kingdom Berkeley Center for Cosmological Physics Department of Physics University of California BerkeleyCA94720 United States Lawrence Berkeley National Laboratory One Cyclotron Road BerkeleyCA94720 United States Department of Physics University of Oxford Denys Wilkinson Building Keble Road OxfordOX1 3RH United Kingdom Via Bonomea 265 Trieste34136 Italy Grignano34151 Italy Sezione di Trieste Via Valerio 2 TriesteI-34127 Italy School of Physics and Astronomy Cardiff University The Parade Wales CardiffCF24 3AA United Kingdom Université de Genève Département de Physique Théorique Cap 24 Quai Ansermet Genève 4CH-1211 Switzerland Research Center for the Early Universe School of Science The University of Tokyo Tokyo113-0033 Japan Jodrell Bank Centre for Astrophysics Department of Physics and Astronomy University of Manchester Alan Turing Building Oxford Road ManchesterM13 9PL United Kingdom Department of Physics University of Milano-Bicocca Piazza della Scienza 3 Milano20126 Italy Université de Paris Cnrs Astroparticule et Cosmologie ParisF-75013 France Center for Computational Astrophysics Flatiron Institute 162 5th Avenue New YorkNY10010 United States Van Swinderen Institute for Particle Physics and Gravity University of Groningen Nijen- borgh 4 Groningen9747 AG Netherlands Department of Physics & Astronomy University of Sussex BrightonBN1 9QH United Kingdom Centre for the Universe Perimeter Institute ON WaterlooN2L 2Y5 Canada Department of Physics and Astronomy University of Southern California Los AngelesCA90007 United States Department of Physics Southern Methodist Univers

We introduce and validate a delensing framework for the Simons Observatory (SO), which will be used to improve constraints on inflationary gravitational waves (IGWs) by reducing the lensing noise in measurements of the B-modes in CMB polarization. SO will initially observe CMB by using three small aperture telescopes and one large-aperture telescope. While polarization maps from small-aperture telescopes will be used to constrain IGWs, the internal CMB lensing maps used to delens will be reconstructed from data from the large-aperture telescope. Since lensing maps obtained from the SO data will be noise-dominated on sub-degree scales, the SO lensing framework constructs a template for lensing-induced B-modes by combining internal CMB lensing maps with maps of the cosmic infrared background from Planck as well as galaxy density maps from the LSST survey. We construct a likelihood for constraining the tensor-to-scalar ratio r that contains auto- and cross-spectra between observed B-modes and the lensing B-mode template. We test our delensing analysis pipeline on map-based simulations containing survey non-idealities, but that, for this initial exploration, does not include contamination from Galactic and extragalactic foregrounds. We find that the SO survey masking and inhomogeneous and atmospheric noise have very little impact on the delensing performance, and the r constraint becomes σ(r) ≈ 0.0015 which is close to that obtained from the idealized forecasts in the absence of the Galactic foreground and is nearly a factor of two tighter than without delensing. We also find that uncertainties in the external large-scale structure tracers used in our multi-tracer delensing pipeline lead to bias much smaller than the 1 σ statistical uncertainties. © 2021, CC BY.

关键词： Observatories

The deterministic and stochastic shallow lake problem

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arXiv 2017年

作者： Kossioris, G.T. Loulakis, M. Souganidis, And P.E. DEPARTMENT OF MATHEMATICS AND APPLIED MATHEMATICS VOUTES CAMPUS UNIVERSITY OF CRETE HERAKLION70013 Greece SCHOOL OF APPLIED MATHEMATICAL AND PHYSICAL SCIENCES NATIONAL TECHNICAL UNIVERSITY OF ATHENS ATHENS15780 Greece INSTITUTE OF APPLIED AND COMPUTATIONAL MATHEMATICS- FOUNDATION OF RESEARCH AND TECHNOLOGY HELLAS HERAKLION700 13 Greece DEPARTMENT OF MATHEMATICS UNIVERSITY OF CHICAGO 5734 S. UNIVERSITY AVENUE CHICAGOIL60637 United States

We study the welfare function of the deterministic and stochastic shallow lake problem. We show that the welfare function is the viscosity solution of the associated Bellman equation, we establish several properties including its asymptotic behaviour at infinity and we present a convergent monotone numerical *** Codes 93E20, 60H10, 49L25 Copyright © 2017, The Authors. All rights reserved.

关键词： Stochastic systems

Clustering with T-SNE, provably

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arXiv 2017年

作者： Linderman, George C. Steinerberger, Stefan Program in Applied Mathematics Yale University New HavenCT06511 United States Department of Mathematics Yale University New HavenCT06511 United States

t-distributed Stochastic Neighborhood Embedding (t-SNE), a clustering and visualization method proposed by van der Maaten &Hinton in 2008, has rapidly become a standard tool in a number of natural sciences. Despite its overwhelming success, there is a distinct lack of mathematical foundations and the inner workings of the algorithm are not well understood. The purpose of this paper is to prove that t-SNE is able to recover well-separated clusters;more precisely, we prove that t-SNE in the 'early exaggeration' phase, an optimization technique proposed by van der Maaten &Hinton (2008) and van der Maaten (2014), can be rigorously analyzed. As a byproduct, the proof suggests novel ways for setting the exaggeration parameter a and step size h. Numerical examples illustrate the effectiveness of these rules: in particular, the quality of embedding of topological structures (e.g. the swiss roll) improves. We also discuss a connection to spectral clustering methods. Copyright © 2017, The Authors. All rights reserved.

关键词： Stochastic systems

A topographic mechanism for arcing of dryland vegetation bands

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arXiv 2018年

作者： Gandhi, Punit Werner, Lucien Iams, Sarah Gowda, Karna Silber, Mary Mathematical Biosciences Institute Ohio State University ColumbusOH43210 United States Department of Computing and Mathematical Sciences California Institute of Technology PasadenaCA91125 United States John A. Paulson School of Engineering and Applied Sciences Harvard University CambridgeMA02138 United States Department of Physics University of Illinois at Urbana-Champaign UrbanaIL61801 United States Committee on Computational and Applied Mathematics Department of Statistics University of Chicago ChicagoIL60637 United States

Banded patterns consisting of alternating bare soil and dense vegetation have been observed in water-limited ecosystems across the globe, often appearing along gently sloped terrain with the stripes aligned transverse to the elevation gradient. In many cases these vegetation bands are arced, with field observations suggesting a link between the orientation of arcing relative to the grade and the curvature of the underlying terrain. We modify the water transport in the Klausmeier model of water-biomass interactions, originally posed on a uniform hillslope, to qualitatively capture the influence of terrain curvature on the vegetation patterns. Numerical simulations of this modified model indicate that the vegetation bands change arcing-direction from convex-downslope when growing on top of a ridge to convex-upslope when growing in a valley. This behavior is consistent with observations from remote sensing data that we present here. Model simulations show further that whether bands grow on ridges, valleys, or both depends on the precipitation level. A survey of three banded vegetation sites, each with a different aridity level, indicates qualitatively similar behavior. Copyright © 2018, The Authors. All rights reserved.

关键词： Ecology

Triangles capturing many lattice points

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arXiv 2017年

作者： Marshall, Nicholas F. Steinerberger, Stefan Program in Applied Mathematics Yale University New HavenCT06511 United States Department of Mathematics Yale University New HavenCT06511 United States

We study a combinatorial problem that recently arose in the context of shape optimization: among all triangles with vertices (0, 0), (x, 0), and (0, y) and fixed area, which one encloses the most lattice points from Z>02? Moreover, does its shape necessarily converge to the isosceles triangle (x = y) as the area becomes large? Laugesen and Liu suggested that, in contrast to similar problems, there might not be a limiting shape. We prove that the limiting set is indeed nontrivial and contains infinitely many elements. We also show that there exist 'bad' areas where no triangle is particularly good at capturing lattice points and show that there exists an infinite set of slopes y/x such that any associated triangle captures more lattice points than any other fixed triangle for infinitely many (and arbitrarily large) areas;this set of slopes is a fractal subset of [1/3, 3] and has Minkowski dimension at most 3/4. Copyright © 2017, The Authors. All rights reserved.

关键词： Shape optimization

SARS-CoV-2 evolution during treatment of chronic infection (vol 592, pg 277, 2021)

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NATURE 2022年第7922期608卷 E23-E23页

作者： Kemp, Steven A. Collier, Dami A. Datir, Rawlings P. Ferreira, Isabella A. T. M. Gayed, Salma Jahun, Aminu Hosmillo, Myra Rees-Spear, Chloe Mlcochova, Petra Lumb, Ines Ushiro Roberts, David J. Chandra, Anita Temperton, Nigel Sharrocks, Katherine Blane, Elizabeth Modis, Yorgo Leigh, Kendra E. Briggs, John A. G. van Gils, Marit J. Smith, Kenneth G. C. Bradley, John R. Smith, Chris Doffinger, Rainer Ceron-Gutierrez, Lourdes Barcenas-Morales, Gabriela Pollock, David D. Goldstein, Richard A. Smielewska, Anna Skittrall, Jordan P. Gouliouris, Theodore Goodfellow, Ian G. Gkrania-Klotsas, Effrossyni Illingworth, Christopher J. R. Mccoy, Laura E. Gupta, Ravindra K. Division of Infection and Immunity University College London London UK Cambridge Institute of Therapeutic Immunology & Infectious Disease (CITIID) Cambridge UK Department of Medicine University of Cambridge Cambridge UK Wellcome Sanger Centre Hinxton UK Department of Biomedicine University and University Hospital Basel Basel Switzerland Botnar Research Centre for Child Health (BRCCH) University Basel & ETH Zurich Basel Switzerland MRC Toxicology Unit School of Biological Sciences University of Cambridge Cambridge UK Medical Research Council Laboratory of Molecular Biology Cambridge UK Africa Health Research Institute Durban South Africa Cambridge Clinical Research Centre NIHR Clinical Research Facility Cambridge University Hospitals NHS Foundation Trust Addenbrooke’s Hospital Cambridge UK Heart and Lung Research Institute Cambridge UK Royal Papworth Hospital NHS Foundation Trust Cambridge UK Department of Applied Mathematics and Theoretical Physics University of Cambridge Cambridge UK Department of Haematology University of Cambridge Cambridge UK Department of Infectious Diseases Cambridge University Hospitals NHS Foundation Trust Cambridge UK Department of Microbiology Cambridge University Hospitals NHS Foundation Trust Cambridge UK NIHR Cambridge Bioresource Cambridge UK Department of Infectious Diseases Cambridge University NHS Hospitals Foundation Trust Cambridge UK Clinical Microbiology and Public Health Laboratory Addenbrooke’s Hospital Cambridge UK Department of Pathology University of Cambridge Cambridge UK Division of Virology Department of Pathology University of Cambridge Cambridge UK Department of Virology Cambridge University NHS Hospitals Foundation Trust Cambridge UK NHS Blood and Transplant Oxford and BRC Haematology Theme University of Oxford Oxford UK Viral Pseudotype Unit Medway School of Pharmacy University of Kent Canterbury UK Department of Medical Microbiology Academic Medical Center University of Amsterdam Amsterdam

Characterizing destructive quantum interference in electron transport

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arXiv 2017年

作者： Sam-Ang, Panu Reuter, Matthew G. Department of Applied Mathematics & Statistics Institute for Advanced Computational Science Stony Brook University Stony BrookNY11794 United States

Destructive quantum interference in electron transport through molecules provides an unconventional route for suppressing electric current. In this work we introduce \interference vectors" for each interference and use them to characterize the interference. An interference vector may be an orbital of the bare molecule, in which case the interference is very sensitive to perturbation. In contrast, an interference vector may be a combination of multiple molecular orbitals, leading to more robust interference that is likelier to be experimentally observable. Our characterization scheme quantifies these two possibilities through the degree of rotation and also assigns an order to each interference that describes the shape of the Landauer-Büttiker transmission function around the interference. Several examples are then presented, showcasing the generality of our theory and characterization scheme, which is not limited to specific classes of molecules or particular molecule-electrode coupling patterns. Copyright © 2017, The Authors. All rights reserved.

关键词： Electron transport properties

Apples with apples comparison of 3+1 conformal numerical relativity schemes

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arXiv 2018年

作者： Daverio, David Dirian, Yves Mitsou, Ermis Centre for Theoretical Cosmology Department of Applied Mathematics and Theoretical Physics Wilberforce Road CambridgeCB3 0WA United Kingdom Department of Theoretical Physics and Center for Astroparticle Physics University of Geneva 24 quai Ansermet Geneve 4CH-1211 Switzerland Center for Theoretical Astrophysics and Cosmology Institute for Computational Science University of Zurich ZurichCH-8057 Switzerland

This paper contains a comprehensive comparison catalog of \Apples with Apples" tests for the BSSNOK, CCZ4 and Z4c numerical relativity schemes, with and without constraint damping terms for the latter two. We use basic numerical methods and reach the same level of accuracy as existing results in the literature. We find that the best behaving scheme is generically CCZ4 with constraint damping terms. Copyright © 2018, The Authors. All rights reserved.

关键词： Fruits

Fluctuating hydrodynamics of electrolytes at electroneutral scales

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arXiv 2018年

作者： Donev, Aleksandar Nonaka, Andrew J. Kim, Changho Garcia, Alejandro L. Bell, John B. Courant Institute of Mathematical Sciences New York University New YorkNY10012 United States Center for Computational Science and Engineering Lawrence Berkeley National Laboratory BerkeleyCA94720 United States Department of Applied Mathematics University of California MercedCA95343 United States Department of Physics San Jose State University San JoseCA95192 United States

At mesoscopic scales electrolyte solutions are modeled by the fluctuating generalized Poisson-Nernst-Planck (PNP) equations [J.-P. Péraud et al., Phys. Rev. F, 1(7):074103, 2016]. However, at length and time scales larger than the Debye scales, electrolytes are effectively electroneutral, and the charged-fluid PNP equations become too stiff to solve numerically. Here we formulate the isothermal incompressible equations of fluctuating hydrodynamics for reactive multispecies mixtures involving charged species in the electroneutral limit, and design a numerical algorithm to solve these equations. Our model does not assume a dilute electrolyte solution but rather treats all species on an equal footing, accounting for cross-diffusion and non-ideality using Maxwell-Stefan theory. By enforcing local electroneutrality as a constraint, we obtain an elliptic equation for the electric potential that replaces the Poisson equation in the fluctuating PNP equations. We develop a second-order midpoint predictor-corrector algorithm to solve either the charged-fluid or electroneutral equations with only a change of the elliptic solver. We use the electroneutral algorithm to study a gravitational fingering instability, triggered by thermal fluctuations, at an interface where an acid and base react to neutralize each other. Our results demonstrate that, because the four ions diffuse with very different coefficients, one must treat each ion as an individual species, and cannot treat the acid, base, and salt as neutral species. This emphasizes the differences between electrodiffusion and classical Fickian diffusion, even at electroneutral scales. Copyright © 2018, The Authors. All rights reserved.

关键词： Electrolytes