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“Skewness and stock option prices”, Hans Gerber and Bruno Landry, July 1997

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North American Actuarial Journal 1998年第2期2卷 114-116页

作者： Kortanek, Kenneth O. Medvedev, V.G. Department of Management Sciences College of Business Administration and Program Applied Mathematical and Computational Sciences University of Iowa Iowa City IA 52242 United States Department of Optimal Control Methods Faculty of Applied Mathematics and Informatics Belorussian State University F Skorina pr 4 Belarus

A hybrid semi-Lagrangian cut cell method for advection-diffusion problems with robin boundary conditions in moving domains

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arXiv 2021年

作者： Barrett, Aaron Fogelson, Aaron L. Griffith, Boyce E. Department of Mathematics University of Utah Salt Lake CityUT United States Departments of Mathematics and Bioengineering University of Utah Salt Lake CityUT 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 Chapel HillNC United States McAllister Heart Institute University of North Carolina Chapel HillNC United States

We present a new discretization approach to advection-diffusion problems with Robin boundary conditions on complex, time-dependent domains. The method is based on second order cut cell finite volume methods introduced by Bochkov et al. [8] to discretize the Laplace operator and Robin boundary condition. To overcome the small cell problem, we use a splitting scheme along with a semi-Lagrangian method to treat advection. We demonstrate second order accuracy in the L1, L2, and L∞norms for both analytic test problems and numerical convergence studies. We also demonstrate the ability of the scheme to convert one chemical species to another across a moving boundary. © 2021, CC BY-SA.

关键词： Advection

Bayesian Parameter Inference for Partially Observed Diffusions using Multilevel Stochastic Runge-Kutta Methods

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arXiv 2023年

作者： Moral, Pierre Del Hu, Shulan Jasra, Ajay Ruzayqat, Hamza Wang, Xinyu Institut de Mathematiques de Bordeaux FR Bordeaux33405 France School of Mathematics and Statistics Wenlan School of Business China Applied Mathematics and Computational Science Program Computer Electrical and Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology Thuwal23955-6900 Saudi Arabia Zhongnan University of Economics and Law CN China

We consider the problem of Bayesian estimation of static parameters associated to a partially and discretely observed diffusion process. We assume that the exact transition dynamics of the diffusion process are unavailable, even up-to an unbiased estimator and that one must time-discretize the diffusion process. In such scenarios it has been shown how one can introduce the multilevel Monte Carlo method to reduce the cost to compute posterior expected values of the parameters for a pre-specified mean square error (MSE);see [12]. These afore-mentioned methods rely on upon the Euler-Maruyama discretization scheme which is well-known in numerical analysis to have slow convergence properties. We adapt stochastic Runge-Kutta (SRK) methods for Bayesian parameter estimation of static parameters for diffusions. This can be implemented in high-dimensions of the diffusion and seemingly under-appreciated in the uncertainty quantification and statistics fields. For a class of diffusions and SRK methods, we consider the estimation of the posterior expectation of the parameters. We prove that to achieve a MSE of O(ϵ2), for ϵ > 0 given, the associated work is O(ϵ−2). Whilst the latter is achievable for the Milstein scheme, this method is often not applicable for diffusions in dimension larger than two. We also illustrate our methodology in several numerical examples. Copyright © 2023, The Authors. All rights reserved.

关键词： Diffusion

Evaluating COVID-19 Surveillance Testing Strategies at Colorado School of Mines: A Stochastic Modeling Approach

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arXiv 2024年

作者： Albrecht, Laura Leiderman, Karin Sindi, Suzanne S. Nychka, Douglas Applied Mathematics and Statistics Department Colorado School of Mines GoldenCO United States Mathematics Department University of North Carolina Chapel Hill Chapel HillNC United States UNC Blood Research Center University of North Carolina Chapel Hill Chapel HillNC United States Computational Medicine Program University of North Carolina Chapel Hill Chapel HillNC United States Department of Applied Mathematics University of California Merced MercedCA United States

This study introduces a stochastic model of COVID-19 transmission tailored to the Colorado School of Mines campus and evaluates surveillance testing strategies within a university context. Enhancing the conventional SEIR framework with stochastic transitions, our model accounts for the unique characteristics of disease spread in a residential college, including specific states for testing, quarantine, and isolation. Employing an approximate Bayesian computation (ABC) method for parameter estimation, we navigate the complexities inherent in stochastic models, enabling an accurate fit of the model with the campus case data. We then studied our model under the estimated parameters to evaluate the efficacy of different testing policies that could be implemented on a university campus. This framework not only advances understanding of COVID-19 dynamics on the Mines campus but serves as a blueprint for comparable settings, providing insights for informed strategies against infectious diseases. © 2024, CC BY.

关键词： COVID-19

Feature selection using stochastic gates

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arXiv 2018年

作者： Yamada, Yutaro Lindenbaum, Ofir Negahban, Sahand Kluger, Yuval Statistics Department Yale University New HavenCT United States Applied Mathematics Program Yale University New HavenCT United States Computational Biology and Bioinformatics Yale University New HavenCT United States Department of Pathology Yale University New HavenCT United States

Feature selection problems have been extensively studied for linear estimation, for instance, Lasso, but less emphasis has been placed on feature selection for non-linear functions. In this study, we propose a method for feature selection in high-dimensional non-linear function estimation problems. The new procedure is based on minimizing the `0 norm of the vector of indicator variables that represent if a feature is selected or not. Our approach relies on the continuous relaxation of Bernoulli distributions, which allows our model to learn the parameters of the approximate Bernoulli distributions via gradient descent. This general framework simultaneously minimizes a loss function while selecting relevant features. Furthermore, we provide an information-theoretic justification of incorporating Bernoulli distribution into our approach and demonstrate the potential of the approach on synthetic and real-life applications. Copyright © 2018, The Authors. All rights reserved.

关键词： Feature extraction

The Athena++ Adaptive Mesh Refinement Framework: Design and Magnetohydrodynamic Solvers

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Astrophysical Journal, Supplement Series 2020年第1期249卷

作者： Stone, James M. Tomida, Kengo White, Christopher J. Felker, Kyle G. Department of Astrophysical Sciences Princeton University Princeton 08544 NJ United States Program in Applied and Computational Mathematics Princeton University Princeton 08544 NJ United States Department of Earth and Space Science Osaka University Toyonaka Osaka 560-0043 Japan Kavli Institute for Theoretical Physics University of California Santa Barbara Santa Barbara 93107 CA United States School of Natural Sciences Institute for Advanced Study Princeton 08544 NJ United States Astronomical Institute Tohoku University Sendai Miyagi 980-8578 Japan Argonne National Laboratory Lemont 60439 IL United States

The design and implementation of a new framework for adaptive mesh refinement calculations are described. It is intended primarily for applications in astrophysical fluid dynamics, but its flexible and modular design enables its use for a wide variety of physics. The framework works with both uniform and nonuniform grids in Cartesian and curvilinear coordinate systems. It adopts a dynamic execution model based on a simple design called a "task list"that improves parallel performance by overlapping communication and computation, simplifies the inclusion of a diverse range of physics, and even enables multiphysics models involving different physics in different regions of the calculation. We describe physics modules implemented in this framework for both nonrelativistic and relativistic magnetohydrodynamics (MHD). These modules adopt mature and robust algorithms originally developed for the Athena MHD code and incorporate new extensions: support for curvilinear coordinates, higher-order time integrators, more realistic physics such as a general equation of state, and diffusion terms that can be integrated with super-time-stepping algorithms. The modules show excellent performance and scaling, with well over 80% parallel efficiency on over half a million threads. The source code has been made publicly available. © 2020. The American Astronomical Society. All rights reserved..

关键词： Astronomy software Magnetohydrodynamics

On Time Uniform Wong-Zakai Approximation Theorems

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arXiv 2023年

作者： Del Moral, Pierre Hu, Shulan Jasra, Ajay Ruzayqat, Hamza Wang, Xinyu Institut de Mathematiques de Bordeaux Bordeaux33405 France School of Statistics and Mathematics Zhongnan University of Economics and Law China Applied Mathematics and Computational Science Program Computer Electrical and Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology Thuwal23955-6900 Saudi Arabia Wenlan School of Business Zhongnan University of Economics and Law China

We consider the long time behavior of Wong-Zakai approximations of stochastic differential equations. These piecewise smooth diffusion approximations are of great importance in many areas, such as those with ordinary differential equations associated to random smooth fluctuations;e.g. robust filtering problems. In many examples, the mean error estimate bounds that have been derived in the literature can grow exponentially with respect to the time horizon. We show in a simple example that indeed mean error estimates do explode exponentially in the time parameter, i.e. in that case a Wong-Zakai approximation is only useful for extremely short time intervals. Under spectral conditions, we present some quantitative time-uniform convergence theorems, i.e. time-uniform mean error bounds, yielding what seems to be the first results of this type for Wong-Zakai diffusion *** Codes 60H35(Primary), 65C30(Secondary) Copyright © 2023, The Authors. All rights reserved.

关键词： Brownian movement

Distinct modes of mitochondrial metabolism uncouple T cell differentiation and function (vol 571, pg 403, 2019)

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NATURE 2019年第7773期573卷 E2-E2页

作者： Bailis, Will Shyer, Justin A. Zhao, Jun Canaveras, Juan Carlos Garcia Al Khazal, Fatimah J. Qu, Rihao Steach, Holly R. Bielecki, Piotr Khan, Omair Jackson, Ruaidhri Kluger, Yuval Maher, Louis J., III Rabinowitz, Joshua Craft, Joe Flavell, Richard A. Department of Immunobiology Yale School of Medicine New Haven USA Department of Pathology Children’s Hospital of Philadelphia Philadelphia USA Department of Pathology Yale School of Medicine New Haven USA Program of Computational Biology and Bioinformatics Yale University New Haven USA Lewis-Sigler Institute for Integrative Genomics Princeton University Princeton USA Department of Chemistry Princeton University Princeton USA Diabetes Research Center University of Pennsylvania Philadelphia USA Department of Biochemistry and Molecular Biology Mayo Clinic College of Medicine and Science Rochester USA Applied Mathematics Program Yale University New Haven USA Department of Internal Medicine (Rheumatology) Yale School of Medicine New Haven USA Howard Hughes Medical Institute Chevy Chase USA

An Amendment to this paper has been published and can be accessed via a link at the top of the paper.

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Modeling global dynamics from local snapshots with deep generative neural networks

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arXiv 2018年

作者： Gigante, Scott Van Dijk, David Moon, Kevin R. Strzalkowski, Alexander Wolf, Guy Krishnaswamy, Smita Computational Biology and Bioinformatics Program Yale University New HavenCT United States Department of Genetics Yale University New HavenCT United States Department of Computer Science Yale University New HavenCT United States Department of Mathematics and Statistics Utah State University LoganUT United States Department of Computer Science Princeton University PrincetonNJ United States Department of Mathematics and Statistics Universitéde Montreacuteal MontéalQC Canada

Complex high dimensional stochastic dynamic systems arise in many applications in the natural sciences and especially biology. However, while these systems are difficult to describe analytically, "snapshot" measurements that sample the output of the system are often available. In order to model the dynamics of such systems given snapshot data, or local transitions, we present a deep neural network framework we call Dynamics Modeling Network or DyMoN. DyMoN is a neural network framework trained as a deep generative Markov model whose next state is a probability distribution based on the current state. DyMoN is trained using samples of current and nextstate pairs, and thus does not require longitudinal measurements. We show the advantage of DyMoN over shallow models such as Kalman filters and hidden Markov models, and other deep models such as recurrent neural networks in its ability to embody the dynamics (which can be studied via perturbation of the neural network) and generate longitudinal hypothetical trajectories. We perform three case studies in which we apply DyMoN to different types of biological systems and extract features of the dynamics in each case by examining the learned model. Copyright © 2018, The Authors. All rights reserved.

关键词： Deep neural networks