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Towards Implementation of the Pressure-Regulated, Feedback-Modulated Model of Star Formation in Cosmological Simulations: Methods and Application to TNG

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arXiv 2024年

作者： Hassan, Sultan Ostriker, Eve C. Kim, Chang-Goo Bryan, Greg L. Burger, Jan D. Fielding, Drummond B. Forbes, John C. Genel, Shy Hernquist, Lars Jeffreson, Sarah M.R. Motwani, Bhawna Smith, Matthew C. Somerville, Rachel S. Steinwandel, Ulrich P. Teyssier, Romain Center for Cosmology and Particle Physics Department of Physics New York University 726 Broadway New YorkNY10003 United States Center for Computational Astrophysics Flatiron Institute 162 5th Ave New YorkNY10010 United States Department of Physics & Astronomy University of the Western Cape Cape Town7535 South Africa Department of Astrophysical Sciences Princeton University PrincetonNJ08544 United States Institute for Advanced Study 1 Einstein Drive PrincetonNJ08540 United States Department of Astronomy Columbia University 550 W 120th Street New YorkNY10027 United States Max-Planck-Institut für Astrophysik Karl-Schwarzschild-Str. 1 GarchingD-85748 Germany Department of Astronomy Cornell University IthacaNY14853 United States School of Physical and Chemical Sciences-Te Kura Matū University of Canterbury Private Bag 4800 Christchurch8140 New Zealand Columbia Astrophysics Laboratory Columbia University 550 West 120th Street New YorkNY10027 United States Center for Astrophysics Harvard & Smithsonian 60 Garden Street CambridgeMA United States Program in Applied and Computational Mathematics Princeton University Fine Hall Washington Road PrincetonNJ08544-1000 United States

Traditional star formation subgrid models implemented in cosmological galaxy formation simulations, such as that of Springel & Hernquist (2003, hereafter SH03), employ adjustable parameters to satisfy constraints measured in the local Universe. In recent years, however, theory and spatially-resolved simulations of the turbulent, multiphase, star-forming ISM have begun to produce new first-principles models, which when fully developed can replace traditional subgrid prescriptions. This approach has advantages of being physically motivated and predictive rather than empirically tuned, and allowing for varying environmental conditions rather than being tied to local Universe conditions. As a prototype of this new approach, by combining calibrations from the TIGRESS numerical framework with the Pressure-Regulated Feedback-Modulated (PRFM) theory, simple formulae can be obtained for both the gas depletion time and an effective equation of state. Considering galaxies in TNG50, we compare the "native" simulation outputs with post-processed predictions from PRFM. At TNG50 resolution, the total midplane pressure is nearly equal to the total ISM weight, indicating that galaxies in TNG50 are close to satisfying vertical equilibrium. The measured gas scale height is also close to theoretical equilibrium predictions. The slopes of the effective equations of states are similar, but with effective velocity dispersion normalization from SH03 slightly larger than that from current TIGRESS simulations. Because of this and the decrease in PRFM feedback yield at high pressure, the PRFM model predicts shorter gas depletion times than the SH03 model at high densities and redshift. Our results represent a first step towards implementing new, numerically calibrated subgrid algorithms in cosmological galaxy formation simulations. Copyright © 2024, The Authors. All rights reserved.

关键词： Cosmology

Hyper-molecules: On the representation and recovery of dynamical structures, with application to flexible macro-molecular structures in cryo-EM

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arXiv 2019年

作者： Lederman, Roy R. Andén, Joakim Singer, Amit Department of Statistics and Data Science Yale University New HavenCT United States Center for Computational Mathematics Flatiron Institute New YorkNY United States Department of Mathematics and Program in Applied and Computational Mathematics Princeton University PrincetonNJ United States

Cryo-electron microscopy (cryo-EM), the subject of the 2017 Nobel Prize in Chemistry, is a technology for determining the 3-D structure of macromolecules from many noisy 2-D projections of instances of these macromolecules, whose orientations and positions are unknown. The molecular structures are not rigid objects, but flexible objects involved in dynamical processes. The different conformations are exhibited by different instances of the macromolecule observed in a cryo-EM experiment, each of which is recorded as a particle image. The range of conformations and the conformation of each particle are not known a priori;one of the great promises of cryo-EM is to map this conformation space. Remarkable progress has been made in determining rigid structures from homogeneous samples of molecules in spite of the unknown orientation of each particle image and significant progress has been made in recovering a few distinct states from mixtures of rather distinct conformations, but more complex heterogeneous samples remain a major challenge. We introduce the "hyper-molecule" framework for modeling structures across different states of heterogeneous molecules, including continuums of states. The key idea behind this framework is representing heterogeneous macromolecules as high-dimensional objects, with the additional dimensions representing the conformation space. This idea is then refined to model properties such as localized heterogeneity. In addition, we introduce an algorithmic framework for recovering such maps of heterogeneous objects from experimental data using a Bayesian formulation of the problem and Markov chain Monte Carlo (MCMC) algorithms to address the computational challenges in recovering these high dimensional hyper-molecules. We demonstrate these ideas in a prototype applied to synthetic data. Copyright © 2019, The Authors. All rights reserved.

关键词： Medical imaging

Predicting permeability via statistical learning on higher-order microstructural information

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arXiv 2020年

作者： Röding, Magnus Ma, Zheng Torquato, Salvatore RISE Research Institutes of Sweden Göteborg41276 Sweden Department of Physics Princeton University PrincetonNJ08544 United States Department of Chemistry Department of Physics Princeton Institute for the Science and Technology of Materials Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

Quantitative structure-property relationships are crucial for the understanding and prediction of the physical properties of complex materials. For fluid flow in porous materials, characterizing the geometry of the pore microstructure facilitates prediction of permeability, a key property that has been extensively studied in material science, geophysics and chemical engineering. In this work, we study the predictability of different structural descriptors via both linear regressions and neural networks. A large data set of 30,000 virtual, porous microstructures of different types, including both granular and continuous solid phases, is created for this end. We compute permeabilities of these structures using the lattice Boltzmann method, and characterize the pore space geometry using one-point correlation functions (porosity, specific surface), two-point surface-surface, surface-void, and void-void correlation functions, as well as the geodesic tortuosity as an implicit descriptor. Then, we study the prediction of the permeability using different combinations of these descriptors. We obtain significant improvements of performance when compared to a Kozeny-Carman regression with only lowest-order descriptors (porosity and specific surface). We find that combining all three two-point correlation functions and tortuosity provides the best prediction of permeability, with the void-void correlation function being the most informative individual descriptor. Moreover, the combination of porosity, specific surface, and geodesic tortuosity provides very good predictive performance. This shows that higher-order correlation functions are extremely useful for forming a general model for predicting physical properties of complex materials. Additionally, our results suggest that artificial neural networks are superior to the more conventional regression methods for establishing quantitative structure-property relationships. We make the data and code used publicly available to fac

关键词： Forecasting

Multi-target detection with application to cryo-electron microscopy

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arXiv 2019年

作者： Bendory, Tamir Boumal, Nicolas Leeb, William Levin, Eitan Singer, Amit Program in Applied and Computational Mathematics Princeton University PrincetonNJ United States Department of Mathematics Princeton University PrincetonNJ United States School of Mathematics University of Minnesota MinneapolisMN United States

We consider the multi-target detection problem of recovering a set of signals that appear multiple times at unknown locations in a noisy measurement. In the low noise regime, one can estimate the signals by first detecting occurrences, then clustering and averaging them. In the high noise regime, however, neither detection nor clustering can be performed reliably, so that strategies along these lines are destined to fail. Notwithstanding, using autocorrelation analysis, we show that the impossibility to detect and cluster signal occurrences in the presence of high noise does not necessarily preclude signal estimation. Specifically, to estimate the signals, we derive simple relations between the autocorrelations of the observation and those of the signals. These autocorrelations can be estimated accurately at any noise level given a sufficiently long measurement. To recover the signals from the observed autocorrelations, we solve a set of polynomial equations through nonlinear least-squares. We provide analysis regarding well-posedness of the task, and demonstrate numerically the effectiveness of the method in a variety of settings. The main goal of this work is to provide theoretical and numerical support for a recently proposed framework to image 3-D structures of biological macromolecules using cryo-electron microscopy in extreme noise levels. Copyright © 2019, The Authors. All rights reserved.

关键词： Autocorrelation

A note on Douglas-Rachford, subgradients, and phase retrieval

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arXiv 2019年

作者： Levin, Eitan Bendory, Tamir Program in Applied and Computational Mathematics Princeton University PrincetonNJ United States School of Electrical Engineering Tel Aviv University Tel Aviv Israel

The properties of gradient techniques for the phase retrieval problem have received a considerable attention in recent years. In almost all applications, however, the phase retrieval problem is solved using a family of algorithms that can be interpreted as variants of Douglas-Rachford splitting. In this work, we establish a connection between Douglas-Rachford and gradient algorithms. Specifically, we show that in some cases a generalization of Douglas-Rachford, called relaxed-reflect-reflect (RRR), can be viewed as subgradient descent on a certain objective function. The solutions coincide with the critical points of that objective, which—in contrast to standard gradient techniques—are not its minimizers. Using the objective function, we analyze the RRR algorithm, describe its set of solutions, show a local convexity around any solution, and derive stability guarantees. Nevertheless, in its present state, the analysis does not elucidate the remarkable empirical performance of RRR and its global properties. Copyright © 2019, The Authors. All rights reserved.

关键词： Machine learning

CONVERGENCE OF A TIME-STEPPING SCHEME TO THE FREE BOUNDARY IN THE SUPERCOOLED STEFAN PROBLEM

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arXiv 2020年

作者： Kaushansky, Vadim Reisinger, Christoph Shkolnikov, Mykhaylo Song, Zhuo Qun Department of Mathematics University of California Los AngelesCA90095 United States Mathematical Institute University of Oxford Andrew Wiles Building Radcliffe Observatory Quarter OxfordOX2 6GG United Kingdom ORFE Department Bendheim Center for Finance and Program in Applied & Computational Mathematics Princeton University Princeton NJ08544 United States Department of Mathematics Princeton University Princeton NJ08544 United States

The supercooled Stefan problem and its variants describe the freezing of a supercooled liquid in physics, as well as the large system limits of systemic risk models in finance and of integrate-and-fire models in neuroscience. Adopting the physics terminology, the supercooled Stefan problem is known to feature a finite-time blow-up of the freezing rate for a wide range of initial temperature distributions in the liquid. Such a blow-up can result in a discontinuity of the liquid-solid boundary. In this paper, we prove that the natural Euler time-stepping scheme applied to a probabilistic formulation of the supercooled Stefan problem converges to the liquid-solid boundary of its physical solution globally in time, in the Skorokhod M1 topology. In the course of the proof, we give an explicit bound on the rate of local convergence for the time-stepping scheme. We also run numerical tests to compare our theoretical results to the practically observed convergence *** Codes 80A22, 35B44, 65N20, 60H30 Copyright © 2020, The Authors. All rights reserved.

关键词： Supercooling

Recursive projection-aggregation decoding of Reed-Muller codes

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arXiv 2019年

作者： Ye, Min Abbe, Emmanuel Mathematics Institute School of Computer and Communication Sciences EPFL Switzerland Program in Applied and Computational Mathematics Department of Electrical Engineering Princeton University Department of Electrical Engineering Princeton University United States

We propose a new class of efficient decoding algorithms for Reed-Muller (RM) codes over binary-input memoryless channels. The algorithms are based on projecting the code on its cosets, recursively decoding the projected codes (which are lower-order RM codes), and aggregating the reconstructions (e.g., using majority votes). We further provide extensions of the algorithms using list-decoding and code concatenation techniques. We run our main algorithm for AWGN channels and Binary Symmetric Channels at the short code length (≤ 1024) and low code rate (≤ 0.5) regime. Simulation results show that the new algorithm not only outperforms the previous decoding algorithms for RM codes, it also outperforms the optimal decoder for polar codes (SCL+CRC) with the same parameters by a wide margin. The performance of the new algorithm for RM codes in those regimes is in fact close to that of the maximal likelihood decoder. Finally, the new decoder naturally allows for parallel implementations. Copyright © 2019, The Authors. All rights reserved.

关键词： Decoding

Advancing electrochemical impedance analysis through innovations in the distribution of relaxation times method

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Joule 2024年第7期8卷 1958-1981页

作者： Maradesa, Adeleke Py, Baptiste Huang, Jake Lu, Yang Iurilli, Pietro Mrozinski, Aleksander Law, Ho Mei Wang, Yuhao Wang, Zilong Li, Jingwei Xu, Shengjun Meyer, Quentin Liu, Jiapeng Brivio, Claudio Gavrilyuk, Alexander Kobayashi, Kiyoshi Bertei, Antonio Williams, Nicholas J. Zhao, Chuan Danzer, Michael Zic, Mark Wu, Phillip Yrjänä, Ville Pereverzyev, Sergei Chen, Yuhui Weber, André Kalinin, Sergei V. Schmidt, Jan Philipp Tsur, Yoed Boukamp, Bernard A. Zhang, Qiang Gaberšček, Miran O'Hayre, Ryan Ciucci, Francesco Department of Mechanical and Aerospace Engineering The Hong Kong University of Science and Technology Hong Kong Metallurgical and Materials Engineering Colorado School of Mines Golden80401 United States Beijing Key Laboratory of Green Chemical Reaction Engineering and Technology Department of Chemical Engineering Tsinghua University Beijing China Green Energy Storage Trento38123 Italy Department of Manufacturing and Production Engineering Faculty of Mechanical Engineering and Ship Technology Institute of Machine and Materials Technology Gdańsk University of Technology Gdańsk Poland Electrode Design for Electrochemical Energy Systems University of Bayreuth Bayreuth Germany School of Chemistry University of New South Wales Sydney Australia School of Advanced Energy Sun Yat-Sen University Shenzhen China Sustainable Energy Center CSEM Neuchâtel2002 Switzerland Interdisciplinary Faculty of Science and Engineering Shimane University Matsue Japan Centre for Electronic and Optical Materials National Institute for Materials Science Tsukuba Japan Department of Civil and Industrial Engineering University of Pisa Pisa Italy Department of Materials Imperial College London Exhibition Road LondonSW7 2AZ United Kingdom Department of Chemical Engineering Massachusetts Institute of Technology Cambridge02139 United States Electrical Energy Systems University of Bayreuth Bayreuth Germany Ruder Boskovic Institute Zagreb Croatia Department of Materials and Minerals Resources Engineering National Taipei University Taipei Taiwan Finland Johann Radon Institute for Computational and Applied Mathematics Linz Austria School of Science and Engineering Nanjing Tech. University Nanjing China Karlsruhe Germany Department of Materials Science and Engineering University of Tennessee KnoxvilleTN37996 United States Physical Science Division Pacific Northwest National Laboratory RichlandWA99354 United States Systems Engineering for Electrical Energy Storage University of B

Electrochemical impedance spectroscopy (EIS) is widely used in electrochemistry, energy sciences, biology, and beyond. Analyzing EIS data is crucial, but it often poses challenges because of the numerous possible equivalent circuit models, the need for accurate analytical models, the difficulties of nonlinear regression, and the necessity of managing large datasets within a unified framework. To overcome these challenges, non-parametric models, such as the distribution of relaxation times (DRT, also known as the distribution function of relaxation times, DFRT), have emerged as promising tools for EIS analysis. For example, the DRT can be used to generate equivalent circuit models, initialize regression parameters, provide a time-domain representation of EIS spectra, and identify electrochemical processes. However, mastering the DRT method poses challenges as it requires mathematical and programming proficiency, which may extend beyond experimentalists’ usual expertise. Post-inversion analysis of DRT data can be difficult, especially in accurately identifying electrochemical processes, leading to results that may not always meet expectations. This article examines non-parametric EIS analysis methods, outlining their strengths and limitations from theoretical, computational, and end-user perspectives, and provides guidelines for their future development. Moreover, insights from survey data emphasize the need to develop a large impedance database, akin to an impedance genome. In turn, software development should target one-click, fully automated DRT analysis for multidimensional EIS spectra interpretation, software validation, and reliability. Particularly, creating a collaborative ecosystem hinged on free software could promote innovation and catalyze the adoption of the DRT method throughout all fields that use impedance data. © 2024 Elsevier Inc.

关键词： Electrochemical impedance spectroscopy

Exponential convergence of the deep neural network approximation for analytic functions Dedicated to Professor Ta Tsien Li on the Occasion of His 80th Birthday

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Science China mathematics 2018年第10期61卷 1733-1740页

作者： Weinan E Qingcan Wang Department of Mathematics and PACM Princeton University Princeton NJ 08544 USA Center for Big Data Research Peking University Beijing 100871 China Beijing Institute of Big Data Research Beijing 100871 China Program in Applied and Computational Mathematics Princeton University Princeton NJ 08544 USA

We prove that for analytic functions in low dimension, the convergence rate of the deep neural network approximation is exponential.

关键词： neural networks approximation theory analytic functions