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Using spatial curvature with HII galaxies and cosmic chronometers to explore the tension in H0

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arXiv 2019年

作者： Ruan, Cheng-Zong Melia, Fulvio Chen, Yu Zhang, Tong-Jie Department of Astronomy Beijing Normal University Beijing100875 China Department of Physics Applied Math Program Department of Astronomy University of Arizona AZ85721 United States Institute for Astronomical Science Dezhou University Dezhou253023 China

We present a model-independent measurement of spatial curvature Ωk in the Friedmann-Lemaître-Robertson-Walker (FLRW) universe, based on observations of the Hubble parameter H(z) using cosmic chronometers, and a Gaussian Process (GP) reconstruction of the HII galaxy Hubble diagram. We show that the imposition of spatial flatness (i.e., Ωk = 0) easily distinguishes between the Hubble constant measured with Planck and that based on the local distance ladder. We find an optimized curvature parameter Ωk = −0.120−+00..168147 when using the former (i.e., H0 = 67.66 ±0.42 km s−1 Mpc−1), and Ωk = −0.298+0−0..122088 for the latter (H0 = 73.24 ± 1.74 km s−1 Mpc−1). The quoted uncertainties are extracted by Monte Carlo sampling, taking into consideration the covariances between the function and its derivative reconstructed by GP. These data therefore reveal that the condition of spatial flatness favours the Planck measurement, while ruling out the locally inferred Hubble constant as a true measure of the large-scale cosmic expansion rate at a confidence level of ∼ 3σ. Copyright © 2019, The Authors. All rights reserved.

关键词： Chronometers

Model-independent test of the cosmic distance duality relation

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arXiv 2018年

作者： Ruan, Cheng-Zong Melia, Fulvio Zhang, Tong-Jie Department of Astronomy Beijing Normal University Beijing100875 China Department of Physics Applied Math Program Department of Astronomy University of Arizona AZ85721 United States Institute for Astronomy Science Dezhou University Dezhou253023 China

A validation of the cosmic distance duality (CDD) relation, η(z)≡ (1+z)2dA(z)/dL(z) = 1, coupling the luminosity (dL) and angular-diameter (dA) distances, is crucial because its violation would require exotic new physics. We present a model-independent test of the CDD, based on strong lensing and a reconstruction of the HII galaxy Hubble diagram using Gaussian Processes, to confirm the validity of the CDD at a very high level of confidence. Using parameterizations η(z) = 1 + η0z and η(z) = 1 + η1z+ η2z2, our best-fit results are η0= 0.0147+0.056-0.066, and η1= 0.1091+0.1680-0.1568and η2= -0.0603+0.0999-0.0988, respectively. In spite of these strong constraints, however, we also point out that the analysis of strong lensing using a simplified single isothermal sphere (SIS) model for the lens produces some irreducible scatter in the inferred CDD data. The use of an extended SIS approximation, with a power-law density structure, yields very similar results, but does not lessen the scatter due to its larger number of free parameters, which weakens the best-fit constraints. Future work with these strong lenses should therefore be based on more detailed ray-tracing calculations to determine the mass distribution more precisely. Copyright © 2018, The Authors. All rights reserved.

关键词： Galaxies

Phase unwinding, or invariant subspace decompositions of hardy spaces

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arXiv 2017年

作者： Coifman, Ronald R. Peyrie, Jacques Department of Mathematics Program in Applied Mathematics Yale University New HavenCT06510 United States Laboratoire de Mathématiques d'Orsay Univ. Paris-Sud CNRS Université Paris-Saclay Orsay91405 France

We consider orthogonal decompositions of invariant subspaces of Hardy spaces, these relate to the Blaschke based phase unwinding decompositions [1, 2, 7]. We prove convergence in Lp. In particular we build an explicit multiscale wavelet basis. We also obtain an explicit unwindinig decomposition for the singular inner function, exp 2iπ/*** Codes 30B50, 30A10, 42C40, 65T99 Copyright © 2017, The Authors. All rights reserved.

关键词： Functions

Analytical/Numerical Solution for the Lagrangian Flamelet Model Equations

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Analytical/Numerical Solution for the Lagrangian Flamelet Mo...

Southern Conference on Computational Modeling (MCSUL)

作者： Francieli Aparecida Vaz Alvaro Luis de Bortoli PPGMAp - Graduate Program in Applied Mathematics UFRGS - Federal University of Rio Grande do Sul Bento Gonçalves 9500 Porto Alegre RS Brazil PPGMAp - Grad. Program in Appl. Math. UFRGS - Fed. Univ. of Rio Grande do Sul Porto Alegre Brazil

In the last years, the understanding of the combustion processes has been facilitated through the progress of asymptotic methods in applied mathematics, of the computation and of experimental techniques. The aim of this work is to obtain and compare analytical/numerical results with experimental data for a confined jet diffusion flame. All thermochemical variables are determined by mixture fraction because the Sandia Flame D, used to check the results, is close to equilibrium. The developed method, based on the low Mach number formulation, allows to decrease the time needed to obtain reasonable results for confined jet diffusion flame. The analytical/numerical results compare well with the experimental data available in the literature.

关键词： Fuels mathematical model Equations Combustion Heating Chemical elements

Cosmological tests with the joint lightcurve analysis

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arXiv 2018年

作者： Melia, F. Wei, J.-J. Maier, R.S. Wu, X.-F. Depts. of Physics and Astronomy Applied Math Program University of Arizona AZ85721 United States Purple Mountain Observatory Chinese Academy of Sciences Nanjing210008 China Depts. of Mathematics and Physics Statistics Program University of Arizona AZ85721 United States Purple Mountain Observatory Nanjing210008 China

We examine whether a comparison between wCDM and Rh = ct using merged Type Ia SN catalogs produces results consistent with those based on a single homogeneous sample. Using the Betoule et al. [1] joint lightcurve analysis (JLA) of a combined sample of 613 events from SNLS and SDSS-II, we estimate the parameters of the two models and compare them. We find that the improved statistics can alter the model selection in some cases, but not others. In addition, based on the model fits, we find that there appears to be a lingering systematic offset of ∼ 0.04-0.08 mag between the SNLS and SDSS-II sources, in spite of the cross-calibration in the JLA. Treating wCDM, ΛCDM and Rh = ct as separate models, we find in an unbiased pairwise statistical comparison that the Bayes Information Criterion (BIC) favors the Rh = ct Universe with a likelihood of 82.8% versus 17.2% for wCDM, but the ratio of likelihoods is reversed (16.2% versus 83.8%) when wde = −1 (i.e., ΛCDM) and strongly reversed (1.0% versus 99.0%) if in addition k = 0 (i.e., flat ΛCDM). We point out, however, that the value of k is a measure of the net energy (kinetic plus gravitational) in the Universe and is not constrained theoretically, though some models of inflation would drive k → 0 due to an expansion-enforced dilution. Since we here consider only the basic ΛCDM model, the value of k needs to be measured and, therefore, the pre-assumption of flatness introduces a significant bias into the BIC. Copyright © 2018, The Authors. All rights reserved.

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Testing viable f(R) models with the angular-diameter distance to compact quasar cores

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Physical Review D 2019年第10期99卷 103505-103505页

作者： Joseph Sultana Fulvio Melia Demosthenes Kazanas Department of Mathematics Faculty of Science University of Malta Msida MSD2080 Malta Department of Physics The Applied Math Program and Department of Astronomy The University of Arizona Tucson Arizona 85721 USA Astrophysics Science Division NASA/Goddard Space Flight Center Greenbelt Maryland 20771 USA

We consider here some popular f(R) models generally viewed as possible alternatives to the existence of dark energy in General Relativity. For each of these, we compute the redshift zmax at which the angular diameter distance dA(z) is expected to reach its maximum value. This turning point in dA(z) was recently measured in a model-independent way using compact quasar cores and was found to occur at zmax=1.70±0.20. We compare the predictions of zmax for the f(R) models with this observed value to test their viability at a deeper level than has been attempted thus far, thereby quantifying an important observational difference between such modified gravity scenarios and standard Lambda Cold Dark Matter (ΛCDM) cosmology. Our results show that, while the most popular f(R) models today are consistent with this measurement to within 1σ, the turning point zmax will allow us to prioritize these alternative gravity theories as the measurement precision continues to improve, particularly with regard to how well they mitigate the tension between the predictions of ΛCDM and the observations. For example, while the Hu-Sawicki version of f(R) increases this tension, the Starobinky model reduces it.

关键词： Alternative gravity theories Cosmological parameters Relativistic aspects of cosmology

Modeling functional cell types in spike train data

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PLoS Computational Biology 2023年第10 October期19卷 e1011509-e1011509页

作者： Zdeblick, Daniel N. Shea-Brown, Eric T. Witten, Daniela M. Buice, Michael A. Department of Electrical and Computer Engineering University of Washington SeattleWA United States Department of Applied Math University of Washington SeattleWA United States MindScope Program Allen Institute SeattleWA United States Department of Statistics and Biostatistics University of Washington SeattleWA United States

A major goal of computational neuroscience is to build accurate models of the activity of neurons that can be used to interpret their function in circuits. Here, we explore using functional cell types to refine single-cell models by grouping them into functionally relevant classes. Formally, we define a hierarchical generative model for cell types, single-cell parameters, and neural responses, and then derive an expectation-maximization algorithm with variational inference that maximizes the likelihood of the neural recordings. We apply this "simultaneous" method to estimate cell types and fit single-cell models from simulated data, and find that it accurately recovers the ground truth parameters. We then apply our approach to in vitro neural recordings from neurons in mouse primary visual cortex, and find that it yields improved prediction of single-cell activity. We demonstrate that the discovered cell-type clusters are well separated and generalizable, and thus amenable to interpretation. We then compare discovered cluster memberships with locational, morphological, and transcriptomic data. Our findings reveal the potential to improve models of neural responses by explicitly allowing for shared functional properties across neurons. Copyright: © 2023 Zdeblick et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

关键词： Neurons

Differentiable unsupervised feature selection based on a gated laplacian 21

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Differentiable unsupervised feature selection based on a gat...

Proceedings of the 35th International Conference on Neural Information Processing Systems

作者： Ofir Lindenbaum Uri Shaham Erez Peterfreund Jonathan Svirsky Nicolas Casey Yuval Kluger Faculty of Engineering Bar-Ilan University Ramat Gan Israel Center for Outcome Research and Evaluation Yale University New Haven CT Hebrew University Independent Researcher University of Pennsylvania Program in Applied Math Department of Pathology Yale University New Haven CT

ISBN: (纸本)9781713845393

Scientific observations may consist of a large number of variables (features). Selecting a subset of meaningful features is often crucial for identifying patterns hidden in the ambient space. In this paper, we present a method for unsupervised feature selection, and we demonstrate its advantage in clustering, a common unsupervised task. We propose a differentiable loss that combines a graph Laplacian-based score that favors low-frequency features with a gating mechanism for removing nuisance features. Our method improves upon the naive graph Laplacian score by replacing it with a gated variant computed on a subset of low-frequency features. We identify this subset by learning the parameters of continuously relaxed Bernoulli variables, which gate the entire feature space. We mathematically motivate the proposed approach and demonstrate that it is crucial to compute the graph Laplacian on the gated inputs rather than on the full feature space in the high noise regime. Using several real-world examples, we demonstrate the efficacy and advantage of the proposed approach over leading baselines.

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Model selection using time-delay lenses

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arXiv 2022年

作者： Melia, Fulvio Wei, Jun-Jie Wu, Xue-Feng Department of Physics The Applied Math Program Department of Astronomy The University of Arizona AZ85721 United States Purple Mountain Observatory Chinese Academy of Sciences Nanjing210023 China School of Astronomy and Space Sciences University of Science and Technology of China Hefei230026 China

The sample of time-delay gravitational lenses appropriate for studying the geometry of the Universe continues to grow as dedicated campaigns, such as the Dark Energy Survey, the VST ATLAS survey, and the Large Synoptic Survey Telescope, complete their census of high-redshift sources. This catalog now includes hundreds of strong lensing systems, at least 31 of which have reasonably accurate time delay measurements. In this paper, we use them to compare the predictions of two competing Friedmann-Lemaître-Robertson-Walker models: flat ΛCDM, characterized by two adjustable parameters (H0 and Ωm), and the Rh = ct universe (with H0 as the single free variable). Over the past decade, the latter has accounted for the data better than the standard model, most recently the emergence of well-formed galaxies discovered by JWST at cosmic dawn. Here we show that the current sample of time-delay lenses favours Rh = ct with a likelihood of ∼ 84% versus ∼ 16% for the standard model. This level of accuracy will greatly improve as the ongoing surveys uncover many thousands additional lens systems over the next several years. © 2022, CC BY.

关键词： Time delay