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arXiv 2021年

作者： Lee, Jae H. Griffith, Boyce E. Department of Mathematics University of North Carolina Chapel HillNC United States Department of Mechanical Engineering Johns Hopkins University BaltimoreMD United States Institute for Computational Medicine Johns Hopkins University BaltimoreMD United States Departments of Mathematics Applied Physical Sciences and Biomedical Engineering University of North Carolina Chapel HillNC United States Carolina Center for Interdisciplinary Applied Mathematics University of North Carolina Chapel HillNC United States Computational Medicine Program University of North Carolina School of Medicine Chapel HillNC United States McAllister Heart Institute University of North Carolina School of Medicine Chapel HillNC United States

The immersed boundary (IB) method is a non-body conforming approach to fluid-structure interaction (FSI) that uses an Eulerian description of the momentum, viscosity, and incompressibility of a coupled fluid-structure system and a Lagrangian description of the deformations, stresses, and resultant forces of the immersed structure. Integral transforms with Dirac delta function kernels couple the Eulerian and Lagrangian variables, and in practice, discretizations of these integral transforms use regularized delta function kernels. Many different kernel functions have been proposed, but prior numerical work investigating the impact of the choice of kernel function on the accuracy of the methodology has often been limited to simplified test cases or Stokes flow conditions that may not reflect the method’s performance in applications, particularly at intermediate-to-high Reynolds numbers, or under different loading conditions. This work systematically studies the effect of the choice of regularized delta function in several fluid-structure interaction benchmark tests using the immersed finite element/difference (IFED) method, which is an extension of the IB method that uses a finite element structural discretizations combined with a Cartesian grid finite difference method for the incompressible Navier-Stokes equations. Whereas the conventional IB method spreads forces from the nodes of the structural mesh and interpolates velocities to those nodes, the IFED formulation evaluates the regularized delta function on a collection of interaction points that can be chosen to be denser than the nodes of the Lagrangian mesh. This opens the possibility of using structural discretizations with wide node spacings that would produce gaps in the Eulerian force in nodally coupled schemes (e.g., if the node spacing is comparable to or broader than the support of the regularized delta function). Earlier work with this methodology suggested that such coarse structural meshes can yield imp

关键词： Fluid structure interaction

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Position: Bayesian deep learning is needed in the age of large-scale AI 24

Position: Bayesian deep learning is needed in the age of lar...

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Proceedings of the 41st International Conference on Machine Learning

作者： Theodore Papamarkou Maria Skoularidou Konstantina Palla Laurence Aitchison Julyan Arbel David Dunson Maurizio Filippone Vincent Fortuin Philipp Hennig José Miguel Hernández-Lobato Aliaksandr Hubin Alexander Immer Theofanis Karaletsos Mohammad Emtiyaz Khan Agustinus Kristiadi Yingzhen Li Stephan Mandt Christopher Nemeth Michael A. Osborne Tim G. J. Rudner David Rügamer Yee Whye Teh Max Welling Andrew Gordon Wilson Ruqi Zhang Department of Mathematics The University of Manchester Manchester UK Eric and Wendy Schmidt Center Broad Institute of MIT and Harvard Cambridge Spotify London UK Computational Neuroscience Unit University of Bristol Bristol UK Centre Inria de l'Université Grenoble Alpes Grenoble France Department of Statistical Science Duke University Statistics Program KAUST Saudi Arabia Helmholtz AI Munich Germany and Department of Computer Science Technical University of Munich Munich Germany and Munich Center for Machine Learning Munich Germany Tübingen AI Center University of Tübingen Tübingen Germany Department of Engineering University of Cambridge Cambridge UK Department of Mathematics University of Oslo Oslo Norway and Bioinformatics and Applied Statistics Norwegian University of Life Sciences Ås Norway Department of Computer Science ETH Zurich Switzerland Chan Zuckerberg Initiative California Center for Advanced Intelligence Project RIKEN Tokyo Japan Vector Institute Toronto Canada Department of Computing Imperial College London London UK Department of Computer Science UC Irvine Irvine Department of Mathematics and Statistics Lancaster University Lancaster UK Department of Engineering Science University of Oxford Oxford UK Center for Data Science New York University New York Munich Center for Machine Learning Munich Germany and Department of Statistics LMU Munich Munich Germany DeepMind London UK and Department of Statistics University of Oxford Oxford UK Informatics Institute University of Amsterdam Amsterdam Netherlands Courant Institute of Mathematical Sciences and Center for Data Science Computer Science Department New York University New York Department of Computer Science Purdue University West Lafayette

In the current landscape of deep learning research, there is a predominant emphasis on achieving high predictive accuracy in supervised tasks involving large image and language datasets. However, a broader perspective reveals a multitude of overlooked metrics, tasks, and data types, such as uncertainty, active and continual learning, and scientific data, that demand attention. Bayesian deep learning (BDL) constitutes a promising avenue, offering advantages across these diverse settings. This paper posits that BDL can elevate the capabilities of deep learning. It revisits the strengths of BDL, acknowledges existing challenges, and highlights some exciting research avenues aimed at addressing these obstacles. Looking ahead, the discussion focuses on possible ways to combine large-scale foundation models with BDL to unlock their full potential.

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Map equation with metadata: Varying the role of attributes in community detection

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Physical Review E 2019年第2期100卷 022301-022301页

作者： Scott Emmons Peter J. Mucha Carolina Center for Interdisciplinary Applied Mathematics Department of Mathematics University of North Carolina Chapel Hill North Carolina 27599 USA

Much of the community detection literature studies structural communities, communities defined solely by the connectivity patterns of the network. Often networks contain additional metadata which can inform community detection such as the grade and gender of students in a high school social network. In this work, we introduce a tuning parameter to the content map equation that allows users of the Infomap community detection algorithm to control the metadata's relative importance for identifying network structure. On synthetic networks, we show that our algorithm can overcome the structural detectability limit when the metadata are well aligned with community structure. On real-world networks, we show how our algorithm can achieve greater mutual information with the metadata at a cost in the traditional map equation. Our tuning parameter, like the focusing knob of a microscope, allows users to “zoom in” and “zoom out” on communities with varying levels of focus on the metadata.

关键词： Clustering Community structure Social networks Block models

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The 230 GHz Variability of Numerical Models of Sagittarius A* II. The Physical Origins of the Variability

arXiv

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arXiv 2024年

作者： Chan, Ho-Sang Chan, Chi-Kwan JILA University of Colorado National Institute of Standards and Technology 440 UCB BoulderCO80309-0440 United States Department of Astrophysical and Planetary Sciences University of Colorado 391 UCB BoulderCO80309 United States Steward Observatory Department of Astronomy University of Arizona 933 N. Cherry Avenue TucsonAZ85721 United States Data Science Institute University of Arizona 1230 N. Cherry Avenue TucsonAZ85721 United States Program in Applied Mathematics University of Arizona 617 North Santa Rita TucsonAZ85721 United States

We explored in Chan et al. (2024) how the ion-electron temperature ratio affects certain numerical models of Sagittarius A* (Sgr A*). Specifically, we studied these effects in magnetic-dominated regions in magnetic-arrested disk (MAD), focusing on the 3-hour variability at 230 GHz — M∆T. In this study, we investigate how variations in electron temperature prescription parameter, RLow, influence M∆T by analyzing a series of general-relativistic raytracing (GRRT) snapshots. In certain black hole models with a spin a > 0, we discover that increasing RLow renders the photon ring more optically thick, obscuring the varying accretion flows that contribute to the variability. However, as RLow increases further, MAD flux eruptions become more pronounced, compensating for the decrease in M∆T. For models with a spin a Low also increases the optical thickness of the fluid, voids within the optically thick gas fail to cover the entire photon ring. Similarly, flux eruptions are more prominent as RLow increases further, contributing to the observed rise in M∆T against RLow. For black holes with a ≈ 0, although the effect of increasing optical depth is still present, their 230 GHz light curves and hence M∆T are insensitive to the changes in RLow. Furthermore, we find that the variability of the 230 GHz light curves at RLow = 1 correlates with fluctuations in the internal energy of the gas near the black hole, indicating that unusual gas heating may be the source of significant M∆T seen in simulations. Our findings highlight potential approaches for refining M∆T to better align with observations when modelling Sgr A* or other low-luminosity active galactic nuclei. © 2024, CC BY.

关键词： Photons

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Isospin symmetry breaking in the charge radius difference of mirror nuclei

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Physical Review C 2022年第6期106卷 L061306-L061306页

作者： Tomoya Naito Xavier Roca-Maza Gianluca Colò Haozhao Liang Hiroyuki Sagawa RIKEN Interdisciplinary Theoretical and Mathematical Sciences Program (iTHEMS) Wako 351-0198 Japan Department of Physics Graduate School of Science The University of Tokyo Tokyo 113-0033 Japan Dipartimento di Fisica Università degli Studi di Milano and INFN Via Celoria 16 20133 Milano Italy Center for Mathematics and Physics University of Aizu Aizu-Wakamatsu 965-8560 Japan RIKEN Nishina Center Wako 351-0198 Japan

Isospin symmetry breaking (ISB) effects in the charge radius difference ΔRch of mirror nuclei are studied using the test example of Ca48 and Ni48. This choice allows for a transparent study of ISB contributions since pairing and deformation effects, commonly required for the study of mirror nuclei, can be neglected in this specific pair. The connection of ΔRch with the nuclear equation of state and the effect of ISB on such a relation are discussed according to an energy density functional approach. We find that nuclear ISB effects may shift the estimated value for the symmetry energy slope parameter L by about 6 to 14 MeV while Coulomb corrections can be neglected. ISB effects on the ground-state energy and charge radii in mirror nuclei have been recently predicted by ab initio calculations to be relatively small, pointing to a negligible effect for the extraction of information on the nuclear EoS. These contrasting results call for a dedicated theoretical effort to solve this overarching problem that impacts not only the neutron-skin thickness or the difference in mass and charge radii of mirror nuclei but also other observables such as the isobaric analog state energy.

关键词： Equations of state of nuclear matter Nuclear density functional theory Symmetry energy

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Block Ratio Optimized Cationic Polyacrylamides for Enhanced Nitrate Rejection Under applied Potential

SSRN

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SSRN 2025年

作者： Vahid, Hossein Hashemi, Arsalan Khavani, Mohammad Sharma, Abhinav Mofrad, Mohammad R.K. Ala-Nissila, Tapio Leibniz-Institut für Polymerforschung Dresden Institut Theory der Polymere Dresden01069 Germany Department of Applied Physics Aalto University P.O. Box 15600 AaltoFI-00076 Finland Molecular Cell Biomechanics Laboratory Departments of Bioengineering and Mechanical Engineering University of California Berkeley BerkeleyCA United States Faculty of Mathematics Natural Sciences and Materials Engineering Institute of Physics University of Augsburg Universitätsstraße 1 Augsburg86159 Germany Molecular Biophysics and Integrative Bioimaging Division Lawrence Berkeley National Laboratory BerkeleyCA United States Quantum Technology Finland Center of Excellence Department of Applied Physics Aalto University P.O. Box 15600 AaltoFI-00076 Finland Interdisciplinary Centre for Mathematical Modelling Department of Mathematical Sciences Loughborough University Loughborough LeicestershireLE11 3TU United Kingdom

The integration of charged polymers and reverse osmosis (RO) membranes presents a promising approach to capture undesired ions and enhance water purification efficiency. In this paper, di-block cationic polyacrylamides (DCPAMs) as charged polymers are evaluated separately in bulk solution and within the RO process to capture nitrite ions introduced by NaNO3. To achieve this, molecular dynamics simulations are conducted to systematically investigate the effects of polymer configuration, concentration, and salt concentration on ion adsorption and water purification performance. The results reveal that nitrate ions exhibit strong adsorption to the charged polymers, leading to the displacement of chloride ions into the bulk solution. The polymer conformations are found to play a critical role in the performance of the process. When an electric potential is applied, anions are strongly attracted to the electrode with a total positive charge, and nitrate ions remain closer to the electrode surface than other *** simultaneous application of RO membranes and DCPAMs achieves salt rejection efficiencies ranging from 78% to 100%, depending on DCPAM type and salt concentration. These findings pave the way for further computational studies on combined processes to advance water purification technologies. © 2025, The Authors. All rights reserved.

关键词： Molecular dynamics

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Inorganic oxides characteristics synthesized from natural limestone found in Aceh Province

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AIP Conference Proceedings 2024年第1期3027卷

作者： Muhammad Rizal Muliadi Ramli Indri Badria Adilina Surya Lubis Rara Mitaphonna Department of Chemistry University of Syiah Kuala Faculty of Mathematics and Natural Sciences 23111 Banda Aceh Aceh Indonesia Research Center for Chemistry National Research and Innovation Agency Kawasan Puspiptek Serpong Serpong Tangerang Selatan 15314 Banten Indonesia Doctoral Program of Mathematics and Applied Sciences Universitas Syiah Kuala 23111 Banda Aceh Aceh Indonesia

This study is focused on the utilization of the limestone from Aceh province, Indonesia, as a raw material for preparing inorganic oxide using a high thermal decomposition method. In this preliminary experiment, the limestone material was powdered, then calcined at a temperature of 900 °C for 4 hours under atmospheric pressure and modified with several concentrations of nickel element (1, 3, 5 wt%). The prepared catalyst was characterized using analytical instruments, namely X-Ray Diffraction (XRD) and Scanning Electron Microscope Energy Dispersive Spectroscopy (SEM-EDS). Based on the diffractogram of XRD, it can be known that the prepared catalyst was dominated by CaO crystals, in which Al2O3 was a minor compound. Characterization of the prepared catalyst using SEM-EDS demonstrated that the catalyst has a homogeneous morphology and uniform particle size.

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Applications of mean field games in financial engineering and economic theory

arXiv

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arXiv 2020年

作者： Carmona, René DEPARTMENT OF OPERATIONS RESEARCH & FINANCIAL ENGINEERING BENDHEIM CENTER FOR FINANCE PROGRAM IN APPLIED & COMPUTATIONAL MATHEMATICS PRINCETON UNIVERSITY United States

This is an expanded version of the lecture given at the AMS Short Course on Mean Field Games, on January 13, 2020 in Denver CO. The assignment was to discuss applications of Mean Field Games in finance and economics. I need to admit upfront that several of the examples reviewed in this chapter were already discussed in book form. Still, they are here accompanied with discussions of, and references to, works which appeared over the last three years. Moreover, several completely new sections are added to show how recent developments in financial engineering and economics can benefit from being viewed through the lens of the Mean Field Game paradigm. The new financial engineering applications deal with bitcoin mining and the energy markets, while the new economic applications concern models offering a smooth transition between macro-economics and finance, and contract *** Codes 60, 91 © 2020, CC BY.

关键词： Finance

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Liquid-liquid transition in water from first principles

arXiv

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arXiv 2022年

作者： Gartner, Thomas E. Piaggi, Pablo M. Car, Roberto Panagiotopoulos, Athanassios Z. Debenedetti, Pablo G. Department of Chemistry Princeton University PrincetonNJ08544 United States Department of Physics Princeton University PrincetonNJ08544 United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Princeton Institute for the Science and Technology of Materials Princeton University PrincetonNJ08544 United States Department of Chemical and Biological Engineering Princeton University PrincetonNJ08544 United States

A longstanding question in water research is the possibility that supercooled liquid water can undergo a liquid-liquid phase transition (LLT) into high- and low-density liquids. We used several complementary molecular simulation techniques to evaluate the possibility of an LLT in an ab initio neural network model of water trained on density functional theory calculations with the SCAN exchange correlation functional. We conclusively show the existence of a first-order LLT and an associated critical point in the SCAN description of water, representing the first definitive computational evidence for an LLT in water from first principles. Copyright © 2022, The Authors. All rights reserved.

关键词： Density functional theory

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More Optimal Fractional-Order Stochastic Gradient Descent for Non-Convex Optimization Problems

arXiv

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arXiv 2025年

作者： Partohaghighi, Mohammad Marcia, Roummel Chen, YangQuan Electrical Engineering and Computer Science Graduate Program University of California Merced United States Department of Applied Mathematics University of California Merced MercedCA United States Lab Department of Mechanical Engineering School of Engineering University of California MercedCA95343 United States

Fractional-order stochastic gradient descent (FOSGD) leverages fractional exponents to capture long-memory effects in optimization. However, its utility is often limited by the difficulty of tuning and stabilizing these exponents. We propose 2SED Fractional-Order Stochastic Gradient Descent (2SEDFOSGD), which integrates the Two-Scale Effective Dimension (2SED) algorithm with FOSGD to adapt the fractional exponent in a data-driven manner. By tracking model sensitivity and effective dimensionality, 2SEDFOSGD dynamically modulates the exponent to mitigate oscillations and hasten convergence. Theoretically, for onoconvex optimization problems, this approach preserves the advantages of fractional memory without the sluggish or unstable behavior observed in naïve fractional SGD. Empirical evaluations in Gaussian and α-stable noise scenarios using an autoregressive (AR) model highlight faster convergence and more robust parameter estimates compared to baseline methods, underscoring the potential of dimension-aware fractional techniques for advanced modeling and estimation tasks. © 2025, CC BY.

关键词： Convex optimization

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