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Editorial

Journal of Biological Dynamics 2019年第sup1期13卷 1-1页

作者： Cushing, Jim Elaydi, Saber Department of Mathematics and Interdisciplinary Program in Applied Mathematics University of Arizona Tucson AZ United States

The 6th International Conference on Mathematical Modelling and Analysis of Populations in Biology (ICMA-VI) was held at the University of Arizona, Tucson, Arizona USA on 20-22 October 2017. Plenary addresses were given by Henri Berestycki (Centre d'analyse et de mathématique sociales, Paris, France), Regis Ferriere (Ecology and Evolutionary Biology Department, University of Arizona, Tucson, Arizona, USA), Rosie Fisher (National Center for Atmospheric Research Climate & Global Dynamics, Boulder, Colorado, USA), and Mercedes Pascual (Department of Ecology and Evolution, University of Chicago, Chicago, Illinois, USA). The conference received support from the Department of mathematics, University of Arizona; the Department of Ecology and Evolutionary Biology, University of Arizona; the interdisciplinary program in applied mathematics, University of Arizona; and the Simon A. Levin Mathematical, Computational and Modeling Sciences Center, Arizona State University. [Extracted from the article]

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NPB-REC: A Non-parametric Bayesian Deep-learning Approach for Undersampled MRI Reconstruction with Uncertainty Estimation

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arXiv 2024年

作者： Khawaled, Samah Freiman, Moti The Interdisciplinary program in Applied Mathematics Faculty of Mathematics Technion Israel Institute of Technology Israel The Faculty of Biomedical Engineering Technion Israel Institute of Technology Israel

The ability to reconstruct high-quality images from undersampled MRI data is vital in improving MRI temporal resolution and reducing acquisition times. Deep learning methods have been proposed for this task, but the lack of verified methods to quantify the uncertainty in the reconstructed images hampered clinical applicability. We introduce "NPB-REC", a non-parametric fully Bayesian framework, for MRI reconstruction from undersampled data with uncertainty estimation. We use Stochastic Gradient Langevin Dynamics during training to characterize the posterior distribution of the network parameters. This enables us to both improve the quality of the reconstructed images and quantify the uncertainty in the reconstructed images. We demonstrate the efficacy of our approach on a multi-coil MRI dataset from the fastMRI challenge and compare it to the baseline End-to-End Variational Network (E2E-VarNet). Our approach outperforms the baseline in terms of reconstruction accuracy by means of PSNR and SSIM (34.55, 0.908 vs. 33.08, 0.897, p Copyright © 2024, The Authors. All rights reserved.

关键词： Magnetic resonance imaging

System-Wide Emergency Policy for Transitioning from Main to Secondary Fuel

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System-Wide Emergency Policy for Transitioning from Main to ...

IEEE Conference on Decision and Control

作者： Laurent Pagnier Criston Hyett Robert Ferrando Igal Goldshtein Jean Alisse Lilah Saban Michael Chertkov Graduate Interdisciplinary Program in Applied Mathematics and Department of Mathematics University of Arizona Tucson AZ USA Noga the Israel Independent System Operator Haifa Israel

ISBN: (数字)9798350316339

ISBN: (纸本)9798350316346

Faced with the complexities of managing natural gas-dependent power system amid the surge of renewable integration and load unpredictability, this study explores strategies for navigating emergency transitions to costlier secondary fuels. Our aim is to develop decision-support tools for operators during such exigencies. We approach the problem through a Markov Decision Process (MDP) framework, accounting for multiple uncertainties. These include the potential for dual-fuel generator failures and operator response during high-pressure situations. Additionally, we consider the finite reserves of primary fuel, governed by gas-flow partial differential equations (PDEs) and constrained by nodal pressure. Other factors include the variability in power forecasts due to renewable generation and the economic impact of compulsory load shedding. For tractability, we address the MDP in a simplified context, replacing it by Markov Processes evaluated against a selection of policies and scenarios for comparison. Our study considers two models for the natural gas system: an oversimplified model tracking linepack and a more nuanced model that accounts for gas flow network heterogeneity. The efficacy of our methods is demonstrated using a realistic model replicating Israel’s power-gas infrastructure.

关键词： Renewable energy sources Uncertainty Navigation Biological system modeling Partial differential equations Power systems Fuels Surges Natural gas Load modeling

System-Wide Emergency Policy for Transitioning from Main to Secondary Fuel

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arXiv 2023年

作者： Pagnier, Laurent Hyett, Criston Ferrando, Robert Goldshtein, Igal Alisse, Jean Saban, Lilah Chertkov, Michael Graduate Interdisciplinary Program in Applied Mathematics Department of Mathematics University of Arizona TucsonAZ85721 United States Israel Independent System Operator Haifa Israel

关键词： Markov processes

Downlink Coverage Analysis in a Heterogeneous Cellular Network

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Downlink Coverage Analysis in a Heterogeneous Cellular Netwo...

IEEE Global Communications Conference

作者： Prasanna Madhusudhanan Juan G. Restrepo Youjian (Eugene) Liu Timothy X. Brown Department of Electrical Computer and Energy Engineering University of Colorado Department of Applied Mathematics Interdisciplinary University of Colorado Telecommunications Program University of Colorado

ISBN: (纸本)9781467309202

In this paper, we consider the downlink signal-to-interference-plus-noise ratio (SINR) analysis in a heterogeneous cellular network with K tiers. Each tier is characterized by a base-station (BS) arrangement according to a homogeneous Poisson point process with certain BS density, transmission power, random shadow fading factors with arbitrary distribution, arbitrary path-loss exponent and a certain bias towards admitting the mobile-station (MS). The MS associates with the BS that has the maximum instantaneous biased received power under the open access cell association scheme. For such a general setting, we provide an analytical characterization of the coverage probability at the MS.

关键词： Multi-tier networks Cellular Radio Co-channel Interference Fading channels Poisson point process Cochannel interference Fading channels point operation cellular radio Bahamas Downlink received power Mass spectroscopy Multiple Sclerosis Coverage Cells

Downlink analysis for a heterogeneous cellular network

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Downlink analysis for a heterogeneous cellular network

2014 12th International Symposium on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks, WiOpt 2014

作者： Madhusudhanan, Prasanna Restrepo, Juan G. Liu, Youjian Eugene Brown, Timothy X. Department of Electrical Computer and Energy Engineering University of Colorado Boulder CO 80309-0425 United States Department of Applied Mathematics University of Colorado Boulder CO 80309-0425 United States Interdisciplinary Telecommunications Program University of Colorado Boulder CO 80309-0425 United States

ISBN: (纸本)9783901882630

In this paper, a comprehensive study of the downlink performance in a heterogeneous cellular network (or hetnet) is conducted. A general hetnet model is considered consisting of an arbitrary number of open-access and closed-access tier of base stations (BSs) arranged according to independent homogeneous Poisson point processes. The BSs of each tier have a constant transmission power, random fading coefficient with an arbitrary distribution and arbitrary path-loss exponent of the power-law path-loss model. For such a system, analytical characterizations for the coverage probability and average rate at an arbitrary mobile-station (MS), and average per-tier load are derived for the max-SINR connectivity model. Using stochastic ordering, interesting properties and simplifications for the hetnet downlink performance are derived by relating this connectivity model to the maximum instantaneous received power (MIRP) connectivity model, providing good insights about the hetnets and the downlink performance in these complex networks. Furthermore, the results also demonstrate the effectiveness and analytical tractability of the stochastic geometric approach to study the hetnet performance. © 2014 IFIP.

关键词： Fading channels

Control of Line Pack in Natural Gas System: Balancing Limited Resources under Uncertainty

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arXiv 2023年

作者： Hyett, Criston Pagnier, Laurent Alisse, Jean Sabban, Lilach Goldshtein, Igal Chertkov, Michael Applied Mathematics The University of Arizona United States The University of Arizona United States Paris University France The Technion Israel Institute of Technology The Graduate Interdisciplinary Program in Applied Mathematics The University of Arizona United States

We build and experiment with a realistic but reduced natural gas model of Israel. The system is unusual because (a) it is controlled from a limited number of points which are at, or close to, the gas extraction sites offshore of Israel's Mediterranean coast;(b) control specifies average flux at inlet, not pressure;(c) there are no inland compressors to regulate pressure;(d) power system is the main consumer of gas (70% of Israel's power is generated at gas-fired power plants distributed across the country). Nature of the system suggests that a special attention should be given to understanding dynamics driven by fast transients in gas consumption meeting intraday variations in the electricity demand, and accounting for increasing role of uncertain renewable generation (mainly solar). Based on all of the above we pose and resolve a sequence of dynamic and control challenges, such as: How to time ramping up- and down- injection of gas to guarantee a healthy intra-day line-pack which meets both pressure constraints and gas-extraction patterns? We report simulation results and utilize monotonicity properties of the natural gas flows which render robustness of our conclusions to the uncertainties of the edge withdrawals of gas. © 2023, CC BY-SA.

关键词： Gases

Modeling coexisting GSF and shear instabilities in rotating stars

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arXiv 2021年

作者： Chang, Eonho Garaud, Pascale Department of Applied Mathematics Baskin School of Engineering University of California Santa CruzCA95064 United States Graduate Interdisciplinary Program in Applied Mathematics University of Arizona TucsonAZ85721 United States

Zahn's widely-used model for turbulent mixing induced by rotational shear has recently been validated (with some caveats) in non-rotating shear flows. It is not clear, however, whether his model remains valid in the presence of rotation, even though this was its original purpose. Furthermore, new instabilities arise in rotating fluids, such as the Goldreich-Schubert-Fricke (GSF) instability. Which instability dominates when more than one can be excited, and how they influence each other, were open questions that this paper answers. To do so, we use direct numerical simulations of diffusive stratified shear flows in a rotating triply-periodic Cartesian domain located at the equator of a star. We find that either the GSF instability or the shear instability tends to take over the other in controlling the system, suggesting that stellar evolution models only need to have a mixing prescription for each individual instability, together with a criterion to determine which one dominates. However, we also find that it is not always easy to predict which instability "wins" for given input parameters, because the diffusive shear instability is subcritical, and only takes place if there is a finite-amplitude turbulence "primer" to seed it. Interestingly, we find that the GSF instability can in some cases play the role of this primer, thereby providing a pathway to excite the subcritical shear instability. This can also drive relaxation oscillations, that may be observable. We conclude by proposing a new model for mixing in the equatorial regions of stellar radiative zones due to differential rotation. Copyright © 2021, The Authors. All rights reserved.

关键词： Stability

Physics-informed machine learning with smoothed particle hydrodynamics: Hierarchy of reduced Lagrangian models of turbulence

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Physical Review Fluids 2023年第5期8卷 054602-054602页

作者： Michael Woodward Yifeng Tian Criston Hyett Chris Fryer Mikhail Stepanov Daniel Livescu Michael Chertkov Graduate Interdisciplinary Program in Applied Mathematics University of Arizona Tucson Arizona 85721 USA Department of Mathematics University of Arizona Tucson Arizona 85721 USA Computer Computational and Statistical Sciences Division LANL Los Alamos New Mexico 87544 USA

Building efficient, accurate, and generalizable reduced-order models of developed turbulence remains a major challenge. This manuscript approaches this problem by developing a hierarchy of parameterized reduced Lagrangian models for turbulent flows, and it investigates the effects of enforcing physical structure through smoothed particle hydrodynamics (SPH) versus relying on neural networks (NNs) as universal function approximators. Starting from NN parametrizations of a Lagrangian acceleration operator, this hierarchy of models gradually incorporates a weakly compressible and parameterized SPH framework, which enforces physical symmetries, such as Galilean, rotational, and translational invariances. Within this hierarchy, two new parameterized smoothing kernels are developed to increase the flexibility of the learn-able SPH simulators. For each model we experiment with different loss functions which are minimized using gradient based optimization, where efficient computations of gradients are obtained by using automatic differentiation and sensitivity analysis. Each model within the hierarchy is trained on two data sets associated with weakly compressible homogeneous isotropic turbulence: (1) a validation set using weakly compressible SPH; and (2) a high-fidelity set from direct numerical simulations. Numerical evidence shows that encoding more SPH structure improves generalizability to different turbulent Mach numbers and time shifts, and that including the novel parameterized smoothing kernels improves the accuracy of SPH at the resolved scales.

关键词： Sensitivity analysis