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Evidence of a truncated spectrum in the angular correlation function of the cosmic microwave background

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arXiv 2017年

作者： Melia, F. López-Corredoira, M. Department of Physics Applied Math Program University of Arizona AZ85721 United States Instituto de Astrofísica de Canarias La Laguna TenerifeE-38205 Spain Departamento de Astrofísica Universidad de la Laguna La Laguna TenerifeE-38206 Spain

Aims. The lack of large-angle correlations in the fluctuations of the cosmic microwave background (CMB) conflicts with predictions of slow-roll inflation. But though probabilities (≤ 0.24%) for the missing correlations disfavor the conventional picture at & 3σ, factors not associated with the model itself may be contributing to the tension. Here we aim to show that the absence of large-angle correlations is best explained with the introduction of a non-zero minimum wavenumber kminfor the fluctuation power spectrum P(k). Methods. We assume that quantum fluctuations were generated in the early Universe with a well-defined power spectrum P(k), though with a cutoff kmin≠ 0. We then re-calculate the angular correlation function of the CMB and compare it with Planck observations. Results. The Planck 2013 data rule out a zero kminat a confidence level exceeding 8σ. Whereas purely slow-roll inflation would have stretched all fluctuations beyond the horizon, producing a P(k) with kmin= 0-and therefore strong correlations at all angles-a kmin≠ 0 would signal the presence of a maximum wavelength at the time (tdec) of decoupling. This argues against the basic inflationary paradigm-perhaps even suggesting non-inflationary alternatives-for the origin and growth of perturbations in the early Universe. In at least one competing cosmology, the Rh = ct universe, the inferred kmincorresponds to the gravitational radius at tdec. Copyright © 2017, The Authors. All rights reserved.

关键词： Cosmology

Computational Methods for Single-Particle Electron Cryomicroscopy

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Biomedical Data Science 1000年第1期3卷 163-190页

作者： Amit Singer Fred J. Sigworth 1Department of Mathematics and Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA email: amits@math.princeton.edu 2Departments of Cellular and Molecular Physiology Biomedical Engineering and Molecular Biophysics and Biochemistry Yale University New Haven Connecticut 06520 USA email: fred.sigworth@yale.edu

Single-particle electron cryomicroscopy (cryo-EM) is an increasingly popular technique for elucidating the three-dimensional (3D) structure of proteins and other biologically significant complexes at near-atomic resolution. It is an imaging method that does not require crystallization and can capture molecules in their native states. In single-particle cryo-EM, the 3D molecular structure needs to be determined from many noisy 2D tomographic projections of individual molecules, whose orientations and positions are unknown. The high level of noise and the unknown pose parameters are two key elements that make reconstruction a challenging computational problem. Even more challenging is the inference of structural variability and flexible motions when the individual molecules being imaged are in different conformational states. This review discusses computational methods for structure determination by single-particle cryo-EM and their guiding principles from statistical inference, machine learning, and signal processing, which also play a significant role in many other data science applications.

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Model Selection using Baryon Acoustic Oscillations in the Final SDSS-IV Release

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arXiv 2022年

作者： Melia, F. López-Corredoira, Martin Department of Physics The Applied Math Program Department of Astronomy The University of Arizona AZ85721 United States Instituto de Astrofísica de Canarias La Laguna TenerifeE-38205 Spain Departamento de Astrofísica Universidad de La Laguna La Laguna TenerifeE-38206 Spain

The baryon acoustic oscillation (BAO) peak, seen in the cosmic matter distribution at redshifts up to ∼ 3.5, reflects the continued expansion of the sonic horizon first identified in temperature anisotropies of the cosmic microwave background. The BAO peak position can now be measured to better than ∼ 1% accuracy using galaxies, and ∼ 1.4 − 1.6% precision with Ly-α forrests and the clustering of quasars. In conjunction with the Alcock-Paczý nski (AP) effect, which arises from the changing ratio of angular to spatial/redshift size of (presumed) spherically-symmetric source distributions with distance, the BAO measurement is viewed as one of the most powerful tools to use in assessing the geometry of the Universe. In this paper, we employ five BAO peak measurements from the final release of the Sloan Digital Sky Survey IV, at average redshifts hzi = 0.38, 0.51, 0.70, 1.48 and 2.33, to carry out a direct head-to-head comparison of the standard model, ΛCDM, and one of its principal competitors, known as the Rh = ct universe. For completeness, we complement the AP diagnostic with a volume-averaged distance probe that assumes a constant comoving distance scale rd. Both probes are free of uncertain parameters, such as the Hubble constant, and are therefore ideally suited for this kind of model selection. We find that Rh = ct is favored by these measurements over the standard model based solely on the AP effect, with a likelihood ∼ 75% versus ∼ 25%, while Planck-ΛCDM is favored over Rh = ct based solely on the volume-averaged distance probe, with a likelihood ∼ 80% versus ∼ 20%. A joint analysis using both probes produces an inconclusive outcome, yielding comparable likelihoods to both models. We are therefore not able to confirm with this work that the BAO data, on their own, support an accelerating Universe. Copyright © 2022, The Authors. All rights reserved.

关键词： Acoustic intensity measurement

Investigating Cosmological Models and the Hubble Tension using Localized Fast Radio Bursts

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arXiv 2023年

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

We use the dispersion measure (DM) and redshift measurements of 24 localized fast radio bursts (FRBs) to compare cosmological models and investigate the Hubble tension. Setting a flat prior on the DM contribution from the Milky Way’s halo, DMMWhalo ∈ [5, 80] pc cm-3, the best fit for flat ΛCDM is obtained with a Hubble constant H0 = 95.8+7.8-9.2 km s-1 Mpc-1 and a median matter density Ωm ≈ 0.66. The best fit for the Rh = ct universe is realized with H0 = 94.2+5.6-6.2 km s-1 Mpc-1. We emphasize that the H0 measurement depends sensitively on the DMMWhalo prior. Since flat ΛCDM has one more free parameter, Rh = ct is favored by the Bayesian Information Criterion (BIC) with a likelihood of ∼ 73% versus ∼ 27%. Through simulations, we find that if the real cosmology is ΛCDM, a sample of ∼ 1,150 FRBs in the redshift range 0 h = ct at a 3σ confidence level, while ∼ 550 FRBs would be necessary to rule out ΛCDM if the real cosmology is instead Rh = ct. The required sample sizes are different, reflecting the fact that the BIC imposes a severe penalty on the model with more free parameters. We further adopt a straightforward method of deriving an upper limit to H0, without needing to consider the poorly known probability distribution of the DM contributed by the host galaxy. The theoretical DM contribution from the intergalactic medium (DMIGM) at any z is proportional to H0. Thus, requiring the extragalactic DMext to be larger than DMIGM delimits H0 to the upside. Assuming flat ΛCDM, we have H0 -1 Mpc-1 at a 95% confidence level. © 2023, CC BY.

关键词： Probability distributions

Model-independent distance calibration and curvature measurement using quasars and cosmic chronometers

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arXiv 2019年

作者： Wei, Jun-Jie Melia, Fulvio Purple Mountain Observatory Chinese Academy of Sciences Nanjing210033 China Guangxi Key Laboratory for Relativistic Astrophysics Guangxi University Nanning530004 China University of Chinese Academy of Sciences Beijing100049 China Department of Physics Applied Math Program Department of Astronomy University of Arizona TucsonAZ85721 United States

We present a new model-independent method to determine the spatial curvature and to mitigate the circularity problem affecting the use of quasars as distance indicators. The cosmic-chronometer measurements are used to construct the curvature-dependent luminosity distance DcalL (ΩK, z) using a polynomial fit. Based on the reconstructed DcalL (ΩK, z) and the known ultraviolet versus X-ray luminosity correlation of quasars, we simultaneously place limits on the curvature parameter ΩK and the parameters characterizing the luminosity correlation function. This model-independent analysis suggests that a mildly closed Universe (ΩK = −0.918 ± 0.429) is preferred at the 2.1σ level. With the calibrated luminosity correlation, we build a new data set consisting of 1598 quasar distance moduli, and use these calibrated measurements to test and compare the standard ΛCDM model and the Rh = ct universe. Both models account for the data very well, though the optimized flat ΛCDM model has one more free parameter than Rh = ct, and is penalized more heavily by the Bayes Information Criterion. We find that Rh = ct is slightly favoured over ΛCDM with a likelihood of ∼ 57.7% versus 42.3%. Copyright © 2019, The Authors. All rights reserved.

关键词： Luminance

Cosmology-independent Estimate of the Hubble Constant and Spatial Curvature Using Time-delay Lenses and Quasars

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arXiv 2020年

作者： Wei, Jun-Jie Melia, Fulvio Purple Mountain Observatory Chinese Academy of Sciences Nanjing210023 China Guangxi Key Laboratory for Relativistic Astrophysics Guangxi University Nanning530004 China University of Chinese Academy of Sciences Beijing100049 China Department of Physics Applied Math Program Department of Astronomy University of Arizona TucsonAZ85721 United States

With the distance sum rule in the Friedmann-Lemaître-Robertson-Walker metric, model-independent constraints on both the Hubble constant H0 and spatial curvature ΩK can be obtained using strong lensing time-delay data and Type Ia supernova (SN Ia) luminosity distances. This method is limited by the relative low redshifts of SNe Ia, however. Here, we propose using quasars as distance indicators, extending the coverage to encompass the redshift range of strong lensing systems. We provide a novel and improved method of determining H0 and ΩK simultaneously. By applying this technique to the time-delay measurements of seven strong lensing systems and the known ultraviolet versus X-ray luminosity correlation of quasars, we constrain the possible values of both H0 and ΩK, and find that H0 = 75.3+−32..09 km s−1 Mpc−1 and ΩK = −0.01−+00..1718. The measured ΩK is consistent with zero spatial curvature, indicating that there is no significant deviation from a flat universe. If we use flatness as a prior, we infer that H0 = 75.3+−11..99 km s−1 Mpc−1, representing a precision of 2.5%. If we further combine these data with the 1048 current Pantheon SNe Ia, our model-independent constraints can be further improved to H0 = 75.3+−32..09 km s−1 Mpc−1 and ΩK = 0.05+−00..1614. In every case, we find that the Hubble constant measured with this technique is strongly consistent with the value (∼ 74 km s−1 Mpc−1) measured using the local distance ladder, as opposed to the value optimized by Planck. Copyright © 2020, The Authors. All rights reserved.

关键词： Supernovae

Graph Fourier MMD for Signals on Graphs

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arXiv 2023年

作者： Leone, Samuel Venkat, Aarthi Huguet, Guillaume Tong, Alexander Wolf, Guy Krishnaswamy, Smita Applied Math Program New HavenCT United States Computational Biology & Bioinformatics Program Yale University New HavenCT United States Dept. of Math. & Stat Université de Montréal Mila - Quebec AI Institute MontrealQC Canada Dept. of Comp. Sci. & Oper. Res. Université de Montréal Mila - Quebec AI Institute MontrealQC Canada Department of Computer Science Department of Genetics Yale University New HavenCT United States

While numerous methods have been proposed for computing distances between probability distributions in Euclidean space, relatively little attention has been given to computing such distances for distributions on graphs. However, there has been a marked increase in data that either lies on graph (such as protein interaction networks) or can be modeled as a graph (single cell data), particularly in the biomedical sciences. Thus, it becomes important to find ways to compare signals defined on such graphs. Here, we propose Graph Fourier MMD (GFMMD), a novel distance between distributions and signals on graphs. GFMMD is defined via an optimal witness function that is both smooth on the graph and maximizes difference in expectation between the pair of distributions on the graph. We find an analytical solution to this optimization problem as well as an embedding of distributions that results from this method. We also prove several properties of this method including scale invariance and applicability to disconnected graphs. We showcase it on graph benchmark datasets as well on single cell RNA-sequencing data analysis. In the latter, we use the GFMMD-based gene embeddings to find meaningful gene clusters. We also propose a novel type of score for gene selection called gene localization score which helps select genes for cellular state space characterization. Copyright © 2023, The Authors. All rights reserved.

关键词： Genes

Testing the Rh = ct Universe Jointly with the Redshift-dependent Expansion rate and Angular-diameter and Luminosity Distances

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arXiv 2019年

作者： Wan, Hao-Yi Cao, Shu-Lei Melia, Fulvio Zhang, Tong-Jie Department of Astronomy Beijing Normal University Beijing100875 China Department of Astronomy Beijing Normal University Beijing100875 China Department of Physics Applied Math Program Department of Astronomy University of Arizona AZ85721 United States Department of Astronomy Beijing Normal University Beijing100875 China Institute for Astronomy Science Dezhou University Dezhou253023 China

We use three different data sets, specifically H(z) measurements from cosmic chronometers, the HII-galaxy Hubble diagram, and reconstructed quasar-core angular-size measurements, to perform a joint analysis of three flat cosmological models: the Rh = ct Universe, ΛCDM, and wCDM. For Rh = ct, the 1σ best-fit value of the Hubble constant H0 is 62.336±1.464 km s−1 Mpc−1, which matches previous measurements (∼ 63 km s−1 Mpc−1) based on best fits to individual data sets. For ΛCDM, our inferred value of the Hubble constant, H0 = 67.013 ± 2.578 km s−1 Mpc−1, is more consistent with the Planck optimization than the locally measured value using Cepheid variables, and the matter density Ωm = 0.347 ±0.049 similarly coincides with its Planck value to within 1σ. For wCDM, the optimized parameters are H0 = 64.718 ± 3.088 km s−1 Mpc−1, Ωm = 0.247 ± 0.108 and w = −0.693 ± 0.276, also consistent with Planck. A direct comparison of these three models using the Bayesian Information Criterion shows that the Rh = ct universe is favored by the joint analysis with a likelihood of ∼ 97% versus . 3% for the other two cosmologies. Copyright © 2019, The Authors. All rights reserved.

关键词： Galaxies

On the verification of adaptive three-dimensional multiresolution computations of the magnetohydrodynamic equations

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arXiv 2019年

作者： Gomes, Anna Karina Fontes Domingues, Margarete Oliveira Mendes, Odim Schneider, Kai Post-graduation Program in Applied Computing National Institute for Space Research São José dos Campos Brazil Associated Laboratory for Computing and Applied Mathematics National Institute for Space Research São José dos Campos Brazil Space Geophysics Division National Institute for Space Research São José dos Campos Brazil Institut de Mathématiques de Marseille Aix-Marseille Université CNRS Centrale Marseille I2M UMR 7373

Magnetohydrodynamics is an important tool to study the dynamics of plasma Space Physics. In this context, we introduce a three-dimensional magnetohydrodynamic solver with divergence-cleaning in the adaptive multiresolution CARMEN code. The numerical scheme is based on a finite volume discretization that ensures the conservation of physical quantities. The adaptive multiresolution approach allows for automatic identification of local structures in the numerical solution and thus provides an adaptive mesh refined only in regions where the solution needs more improved resolution. We assess the three-dimensional magnetohydrodynamic CARMEN code and compare its results with the ones from the well-known FLASH code. Copyright © 2019, The Authors. All rights reserved.

关键词： Magnetohydrodynamics