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arXiv 2018年

作者： Singer, Amit Department of Mathematics Program in Applied and Computational Mathematics Princeton University

Single-particle cryo-electron microscopy (cryo-EM) has recently joined X-ray crystallography and NMR spectroscopy as a high-resolution structural method for biological macromolecules. Cryo-EM was selected by Nature Methods as Method of the Year 2015, large scale investments in cryo-EM facilities are being made all over the world, and the Nobel Prize in Chemistry 2017 was awarded to Jacques Dubochet, Joachim Frank and Richard Henderson "for developing cryo-electron microscopy for the high-resolution structure determination of biomolecules in solution". This paper focuses on the mathematical principles underlying existing algorithms for structure determination using single particle cryo-EM.92C55, 68U10, 44A12, 62H12, 33C55, 90C22 Copyright © 2018, The Authors. All rights reserved.

关键词： Electron microscopes

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Optimal frames and Newton's method

Optimal frames and Newton's method

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作者： Fickus, Matthew Mixon, Dustin G. Department of Mathematics Air Force Institute of Technology Wright-Patterson AFB OH 45433 United States Program in Applied and Computational Mathematics Princeton University Princeton NJ United States

Given a parametrized family of finite frames, we consider the optimization problem of finding the member of this family whose coefficient space most closely contains a given data vector. This nonlinear least squares problem arises naturally in the context of a certain type of radar system. We derive analytic expressions for the first and second partial derivatives of the objective function in question, permitting this optimization problem to be efficiently solved using Newton's method. We also consider how sensitive the location of this minimizer is to noise in the data vector. We further provide conditions under which one should expect the minimizer of this objective function to be unique. We conclude by discussing a related variational-calculus- based approach for solving this frame optimization problem over an interval of time. © 2012 Copyright.

关键词： Newton-Raphson method

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Viscosity in water from first-principles and deep-neural-network simulations

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npj computational Materials 2022年第1期8卷 1318-1327页

作者： Cesare Malosso Linfeng Zhang Roberto Car Stefano Baroni Davide Tisi SISSA—Scuola Internazionale Superiore di Studi Avanzati 34136TriesteItaly Program in Applied and Computational Mathematics Princeton UniversityPrincetonNJ08544USA DP Technology Beijing100080PR China Department of Chemistry Department of Physicsand Princeton Institute for the Science and Technology of MaterialsPrinceton UniversityPrincetonNJUSA CNR Istituto Officina dei Materiali SISSA Unit34136TriesteItaly

We report on an extensive study of the viscosity of liquid water at near-ambient conditions,performed within the Green-Kubo theory of linear response and equilibrium ab initio molecular dynamics(AIMD),based on density-functional theory(DFT).In order to cope with the long simulation times necessary to achieve an acceptable statistical accuracy,our ab initio approach is enhanced with deep-neural-network potentials(NNP).This approach is first validated against AIMD results,obtained by using the Perdew–Burke–Ernzerhof(PBE)exchange-correlation functional and paying careful attention to crucial,yet often overlooked,aspects of the statistical data ***,we train a second NNP to a dataset generated from the Strongly Constrained and Appropriately Normed(SCAN)*** the error resulting from the imperfect prediction of the melting line is offset by referring the simulated temperature to the theoretical melting one,our SCAN predictions of the shear viscosity of water are in very good agreement with experiments.

关键词： viscosity Strongly ambient

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Cost-effectiveness of personalized policies for implementing organ-at-risk sparing adaptive radiation therapy in head and neck cancer

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physics and Imaging in Radiation Oncology 2025年 34卷 100772-100772页

作者： Hosseinian, Seyedmohammadhossein Suarez-Aguirre, Daniel Dede, Cem Garcia, Raul McCullum, Lucas Hemmati, Mehdi Karagoz, Aysenur Mohamed, Abdallah S.R. Lai, Stephen Y. Hutcheson, Katherine A. Moreno, Amy C. Brock, Kristy K. Nosrat, Fatemeh Fuller, Clifton D. Schaefer, Andrew J. Edward P. Fitts Department of Industrial and Systems Engineering North Carolina State University Raleigh NC United States Department of Computational Applied Mathematics and Operations Research Rice University Houston TX United States Department of Radiation Oncology The University of Texas MD Anderson Cancer Center Houston TX United States School of Industrial and Systems Engineering University of Oklahoma Norman OK United States Stephenson Cancer Center University of Oklahoma Health Science Center Norman OK United States Department of Radiation Oncology Baylor College of Medicine Houston TX United States Department of Head and Neck Surgery The University of Texas MD Anderson Cancer Center Houston TX United States Department of Imaging Physics The University of Texas MD Anderson Cancer Center Houston TX United States

Background and Purpose: The principle of adaptive radiation therapy (ART) is to adjust radiation plans in response to anatomical changes during treatment. The purpose of this study was to develop a decision-making model for implementation of personalized ART that balances the costs and clinical benefits of radiation plan adaptations in head and neck cancer (HNC). Materials and Methods: Using retrospective imaging data from 52 HNC patients, a Markov decision process (MDP) model was developed to determine optimal timing for plan adaptations based on the difference in normal tissue complication probability (ΔNTCP) between planned and delivered doses to organs-at-risk. To capture the trade-off between the costs and benefits of plan adaptations, the end-treatment ΔNTCPs were converted to Quality Adjusted Life Years (QALYs) and then to equivalent monetary values using a willingness-to-pay per QALY parameter. Results: The optimal policies were derived for 96 combinations of willingness-to-pay per QALY (W) and re-planning cost (RC) and validated using Monte Carlo simulation for two representative scenarios: (1) W = $200,000, RC = $1,000;(2) W = $100,000, RC = $2,000. In scenario (1), the MDP model's policy reduced the probability of excessive toxicity (ΔNTCP ≥ 5 %) to zero (from 0.21 without re-planning) at an average cost of $380 per patient. In scenario (2), it reduced this probability to 0.02 at an average cost of $520 per patient. Conclusions: The MDP model's policies outperformed the current fixed-time (one-size-fits-all) approaches in both clinical and financial outcomes in the simulations. © 2025 The Author(s)

关键词： Cost-effective policies Markov decision processes Optimal resource allocation Organ-at-risk sparing Personalized adaptive radiation therapy

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An expectation-maximization algorithm for continuous-time hidden Markov models

arXiv

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arXiv 2021年

作者： Wang, Qingcan Weinan, E. Program in Applied and Computational Mathematics Princeton University United States Department of Mathematics and Program in Applied and Computational Mathematics Princeton University United States

We propose a unified framework that extends the inference methods for classical hidden Markov models to continuous settings, where both the hidden states and observations occur in continuous time. Two different settings are analyzed: hidden jump process with a finite state space, and hidden diffusion process with a continuous state space. For each setting, we first estimate the hidden states given the observations and model parameters, showing that the posterior distribution of the hidden states can be described by differential equations in continuous time. We then consider the estimation of unknown model parameters, deriving the continuous-time formulas for the expectation-maximization algorithm. We also propose a Monte Carlo method based on the continuous formulation, sampling the posterior distribution of the hidden states and updating the parameter *** Codes 60J25, 65C40 Copyright © 2021, The Authors. All rights reserved.

关键词： Continuous time systems

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Finding disparity map via image pyramid

Finding disparity map via image pyramid

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17th International Conference on Computer Graphics and Vision, GraphiCon 2007

作者： Volegov, Dmitry B. Yurin, Dmitry V. Moscow Institute of Physics and Technology Department of General and Applied Physics Sub-Faculty of SIM Russia FSUE RPE OPTECS Russia Moscow State University Department of Computational Mathematics and Cybernetics Russia

Algorithm for finding disparity map using image pyramid is presented. Stability of algorithm is improved by using image texture information and noise level. Results are presented.

关键词： Image texture

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End-to-end symmetry preserving inter-atomic potential energy model for finite and extended systems 32

End-to-end symmetry preserving inter-atomic potential energy...

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32nd Conference on Neural Information Processing Systems, NeurIPS 2018

作者： Zhang, Linfeng Han, Jiequn Wang, Han Saidi, Wissam A. Car, Roberto Weinan, E. Program in Applied and Computational Mathematics Princeton University United States Institute of Applied Physics and Computational Mathematics China CAEP Software Center for High Performance Numerical Simulation China Department of Mechanical Engineering and Materials Science University of Pittsburgh United States Department of Chemistry Department of Physics Princeton University United States Princeton Institute for the Science and Technology of Materials Princeton University United States Department of Mathematics Princeton University United States Beijing Institute of Big Data Research China

Machine learning models are changing the paradigm of molecular modeling, which is a fundamental tool for material science, chemistry, and computational biology. Of particular interest is the inter-atomic potential energy surface (PES). Here we develop Deep Potential - Smooth Edition (DeepPot-SE), an end-to-end machine learning-based PES model, which is able to efficiently represent the PES of a wide variety of systems with the accuracy of ab initio quantum mechanics models. By construction, DeepPot-SE is extensive and continuously differentiable, scales linearly with system size, and preserves all the natural symmetries of the system. Further, we show that DeepPot-SE describes finite and extended systems including organic molecules, metals, semiconductors, and insulators with high fidelity. © 2018 Curran Associates Inc..All rights reserved.

关键词： Potential energy

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Certified randomness using a trapped-ion quantum processor

arXiv

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arXiv 2025年

作者： Liu, Minzhao Shaydulin, Ruslan Niroula, Pradeep DeCross, Matthew Hung, Shih-Han Kon, Wen Yu Cervero-Martín, Enrique Chakraborty, Kaushik Amer, Omar Aaronson, Scott Acharya, Atithi Alexeev, Yuri Berg, K. Jordan Chakrabarti, Shouvanik Curchod, Florian J. Dreiling, Joan M. Erickson, Neal Foltz, Cameron Foss-Feig, Michael Hayes, David Humble, Travis S. Kumar, Niraj Larson, Jeffrey Lykov, Danylo Mills, Michael Moses, Steven A. Neyenhuis, Brian Eloul, Shaltiel Siegfried, Peter Walker, James Lim, Charles Pistoia, Marco Global Technology Applied Research JPMorganChase New YorkNY10017 United States Quantinuum BroomfieldCO80021 United States Computational Science Division Argonne National Laboratory LemontIL60439 United States Department of Physics The University of Chicago ChicagoIL60637 United States Department of Computer Science The University of Texas at Austin AustinTX78712 United States Department of Electrical Engineering National Taiwan University Taipei City10617 Taiwan Quantinuum Terrington House 13–15 Hills Road CambridgeCB2 1NL United Kingdom Quantum Science Center Oak Ridge National Laboratory Oak RidgeTN37831 United States Mathematics and Computer Science Division Argonne National Laboratory LemontIL60439 United States

While quantum computers have the potential to perform a wide range of practically important tasks beyond the capabilities of classical computers [1, 2], realizing this potential remains a challenge. One such task is to use an untrusted remote device to generate random bits that can be certified to contain a certain amount of entropy [3]. Certified randomness has many applications [4] but is fundamentally impossible to achieve solely by classical computation. In this work, we demonstrate the generation of certifiably random bits using the 56-qubit Quantinuum H2-1 trapped-ion quantum computer accessed over the internet. Our protocol leverages the classical hardness of recent random circuit sampling demonstrations [5, 6]: a client generates quantum "challenge" circuits using a small randomness seed, sends them to an untrusted quantum server to execute, and verifies the server’s results. We analyze the security of our protocol against a restricted class of realistic near-term adversaries. Using classical verification with measured combined sustained performance of 1.1 × 1018 floating-point operations per second across multiple supercomputers, we certify 71, 313 bits of entropy under this restricted adversary and additional assumptions. Our results demonstrate a step towards the practical applicability of today’s quantum computers. Copyright © 2025, The Authors. All rights reserved.

关键词： Quantum computers

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Applicability of 9Be global optical potential to reactions of 7,10,11,12Be

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Chinese physics C 2019年第9期43卷 55-61页

作者： Yong-Li Xu Yin-Lu Han Hai-Ying Liang Zhen-Dong Wu Hai-Rui Guo Chong-Hai Cai College of Physics and Electronic Science Shanxi Datong UniversityDatong 037009China Key Laboratory of Nuclear Data China Institute of Atomic EnergyP.O.BOX(275-41)Beijing 102413China Institute of Applied Physics and Computational Mathematics Beijing 100094China Department of Physics Nankai UniversityTianjin 300071China

Elastic scattering angular distributions and total reaction cross-sections of 7,10,11,12Be projectiles are predicted by the systematic 9Be global phenomenological optical model potential for target mass numbers ranging from 24 to *** predictions provide a detailed analysis by their comparison with the available experimental ***,these elastic scattering observables are also predicted for some targets out of the mass number *** results are in reasonable agreement with the existing experimental data,and they are presented in this study.

关键词： global phenomenological optical model potential elastic scattering angular distributions total reaction cross sections

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Hyperuniformity order metric of Barlow packings

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Physical Review E 2019年第2期99卷 022111-022111页

作者： T. M. Middlemas F. H. Stillinger S. Torquato Department of Chemistry Department of Physics Princeton Institute for the Science and Technology of Materials and Program in Applied and Computational Mathematics Princeton University New Jersey 08544 USA

The concept of hyperuniformity has been a useful tool in the study of density fluctuations at large length scales in systems ranging across the natural and mathematical sciences. One can rank a large class of hyperuniform systems by their ability to suppress long-range density fluctuations through the use of a hyperuniformity order metric Λ¯. We apply this order metric to the Barlow packings, which are the infinitely degenerate densest packings of identical rigid spheres that are distinguished by their stacking geometries and include the commonly known fcc lattice and hcp crystal. The “stealthy stacking” theorem implies that these packings are all stealthy hyperuniform, a strong type of hyperuniformity, which involves the suppression of scattering up to a wave vector K. We describe the geometry of three classes of Barlow packings, two disordered classes and small-period packings. In addition, we compute a lower bound on K for all Barlow packings. We compute Λ¯ for the aforementioned three classes of Barlow packings and find that, to a very good approximation, it is linear in the fraction of fcc-like clusters, taking values between those of least-ordered hcp and most-ordered fcc. This implies that the value of Λ¯ of all Barlow packings is primarily controlled by the local cluster geometry. These results highlight the special nature of anisotropic stacking disorder, which provides impetus for future research on the development of anisotropic order metrics and hyperuniformity properties.

关键词： Classical statistical mechanics

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