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2012 ACM Conference on Bioinformatics, computational Biology and Biomedicine, BCB 2012

作者： Yehdego, Daniel T. Zhang, Boyu Taufer, Michela Kodimala, Vikram Kumar Reddy Vegesna, Rahulsimham Viswakula, Sameera Johnson, Kyle L. Leung, Ming-Ying Computational Science Program University of Texas El Paso United States Department of Computer and Information Sciences University of Delaware United States Bioinformatics Program Border Biomedical Research Center University of Texas El Paso United States Department of Mathematical Sciences University of Texas El Paso United States Department of Biological Sciences University of Texas El Paso United States Department of Mathematics and Statistics Old Dominion University Norfolk VA United States University of Texas M. D. Anderson Cancer Center Houston TX United States

ISBN: (纸本)9781450316705

The tremendous demand on computer memory and computing time for prediction of complex secondary structures limits the applicability of most RNA secondary structure prediction programs available to short RNA sequences. We propose to approach this problem by segmenting a long RNA sequence into shorter non-overlapping chunks, predicting the secondary structures of each chunk individually, and then assembling the prediction results to give the structure of the original sequence. The selection of cutting points is a crucial component of the approach. Noting that stem-loops and pseudoknots always contain an inversion, we developed two cutting methods, the centered and optimized methods, for segmenting long RNA sequences based on inversion excursions. For the majority of the sequences in a dataset of 50 RNAs from the RFAM database, the prediction algorithm PKnotsRG used with these cutting methods produces more accurate secondary structures than those predicted for the whole sequence without segmentation. Both the centered and optimized cutting methods outperform the naïve regular segmentation. These results support our claim that cutting is a promising approach for the prediction of long RNA sequences, and choosing the cutting points intelligently by considering sequence features such as inversion excursions can further enhance prediction accuracy.

关键词： Forecasting

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Stabilizing zero-field skyrmions in Ir/Fe/Co/Pt thin film multilayers by magnetic history control

arXiv

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arXiv 2019年

作者： Duong, Nghiep Khoan Raju, M. Petrović, A.P. Tomasello, R. Finocchio, G. Panagopoulos, Christos Division of Physics and Applied Physics School of Physical and Mathematical Sciences Nanyang Technological University 21 Nanyang Link Singapore637371 Institute of Applied and Computational Mathematics FORTH Heraklion-CreteGR-70013 Greece Department of Mathematical and Computer Sciences Physical Sciences and Earth Sciences University of Messina Messina98166 Italy

We present a study of the stability of room-temperature skyrmions in [Ir/Fe/Co/Pt] thin film multilayers, using the First Order Reversal Curve (FORC) technique and magnetic force microscopy (MFM). FORC diagrams reveal irreversible changes in magnetization upon field reversals, which can be correlated with the evolution of local magnetic textures probed by MFM. Using this approach, we have identified two different mechanisms - (1) skyrmion merger and (2) skyrmion nucleation followed by stripe propagation - which facilitate magnetization reversal in a changing magnetic field. Analysing the signatures of these mechanisms in the FORC diagram allows us to identify magnetic "histories" - i.e. precursor field sweep protocols - capable of enhancing the final zero-field skyrmion density. Our results indicate that FORC measurements can play a useful role in characterizing spin topology in thin film multilayers, and are particularly suitable for identifying samples in which skyrmion populations can be stabilized at zero field. Copyright © 2019, The Authors. All rights reserved.

关键词： Textures

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EXISTENCE OF MAXIMAL SOLUTIONS FOR THE FINANCIAL STOCHASTIC STEFAN PROBLEM OF A VOLATILE ASSET WITH SPREAD

arXiv

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arXiv 2023年

作者： Antonopoulou, D.C. Farazakis, D. Karali, G. Department of Mathematics and Applied Mathematics University of Crete HeraklionGR-714 09 Greece Department of Physical and Mathematical Sciences Engineering University of Chester CH2 4NU United Kingdom Institute of Applied and Computational Mathematics FORTH HeraklionGR-711 10 Greece

In this work, we consider the outer Stefan problem for the short-time prediction of the spread of a volatile asset traded in a financial market. The stochastic equation for the evolution of the density of sell and buy orders is the Heat Equation with a non-smooth noise in the sense of Walsh, posed in a moving boundary domain with velocity given by the Stefan condition. This condition determines the dynamics of the spread, and the solid phase [s−(t), s+(t)] defines the bid-ask spread area wherein the transactions vanish. We introduce a reflection measure and prove existence and uniqueness of maximal solutions up to stopping times in which the spread s+(t)−s−(t) stays a.s. non-negative and bounded. For this, we use a Picard approximation scheme and some of the estimates of [19] for the Green's function and the associated to the reflection measure obstacle problem. Analogous results are obtained for the equation without reflection corresponding to a signed density. Additionally, we apply some formal asymptotics when the noise depends only on time to derive that the spread is given by the integral of the solution of a linear diffusion stochastic *** Codes 35K55, 35K40, 60H30, 60H15, 91G80, 91B70 © 2023, CC BY.

关键词： Stochastic systems

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Embedded domain Reduced Basis Models for the shallow water hyperbolic equations with the Shifted Boundary Method

arXiv

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arXiv 2022年

作者： Zeng, Xianyi Stabile, Giovanni Karatzas, Efthymios N. Scovazzi, Guglielmo Rozza, Gianluigi Department of Mathematical Sciences University of Texas at El Paso United States SISSA International School for Advanced Studies Mathematics Area mathLab Trieste Italy Department of Mathematics School of Applied Mathematical and Physical Sciences NTUA Athens Greece FORTH Institute of Applied and Computational Mathematics Heraclion Crete Greece Civil and Environmental Engineering Department Duke University DurhamNC27708 United States

We consider fully discrete embedded finite element approximations for a shallow water hyperbolic problem and its reduced-order model. Our approach is based on a fixed background mesh and an embedded reduced basis. The Shifted Boundary Method for spatial discretization is combined with an explicit predictor/multi-corrector time integration to integrate in time the numerical solutions to the shallow water equations, both for the full and reduced-order model. In order to improve the approximation of the solution manifold also for geometries that are untested during the offline stage, the snapshots have been pre-processed by means of an interpolation procedure that precedes the reduced basis computation. The methodology is tested on geometrically parametrized shapes with varying size and position. © 2022, CC BY.

关键词： Equations of motion

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Solving Schrödinger Equation Using Tensor Neural Network

arXiv

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arXiv 2022年

作者： Liao, Yangfei Lin, Zhongshuo Liu, Jianghao Sun, Qingyuan Wang, Yifan Wu, Teng Xie, Hehu He, Mingfeng LSEC NCMIS Institute of Computational Mathematics Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China School of Mathematical Sciences University of Chinese Academy of Sciences Beijing100049 China Zhiyuan College Department of Mathematics and Applied Mathematics Shanghai Jiao Tong University Shanghai201100 China School of Mathematical Sciences Peking University Beijing100871 China

In this paper, we introduce a novel approach to solve the many-body Schrödinger equation by the tensor neural network. Based on the tensor product structure, we can do the direct numerical integration by using fixed quadrature points for the functions constructed by the tensor neural network within tolerable computational complexity. Especially, we design several types of efficient numerical methods to treat the variable-coupled Coulomb potentials with high accuracy. The corresponding machine learning method is built for solving many-body Schrödinger equation. Some numerical examples are provided to validate the accuracy and efficiency of the proposed *** Codes 65N25, 65L15, 65B99, 68T07 © 2022, CC BY-NC-ND.

关键词： Schrodinger equation

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Deep potential molecular dynamics: A scalable model with the accuracy of quantum mechanics

arXiv

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arXiv 2017年

作者： Zhang, Linfeng Han, Jiequn Wang, Han Car, Roberto Weinan, E. Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Institute of Applied Physics and Computational Mathematics Fenghao East Road 2 Beijing100094 China CAEP Software Center for High Performance Numerical Simulation Huayuan Road 6 Beijing100088 China Department of Chemistry Department of Physics Program in Applied and Computational Mathematics Princeton Institute for the Science and Technology of Materials Princeton University PrincetonNJ08544 United States Department of Mathematics and Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Center for Data Science Beijing International Center for Mathematical Research Peking University Beijing Institute of Big Data Research Beijing100871 China

We introduce a scheme for molecular simulations, the Deep Potential Molecular Dynamics (DeePMD) method, based on a many-body potential and interatomic forces generated by a carefully crafted deep neural network trained with ab initio data. The neural network model preserves all the natural symmetries in the problem. It is "first principle-based" in the sense that there are no ad hoc components aside from the network model. We show that the proposed scheme provides an efficient and accurate protocol in a variety of systems, including bulk materials and molecules. In all these cases, DeePMD gives results that are essentially indistinguishable from the original data, at a cost that scales linearly with system size. Copyright © 2017, The Authors. All rights reserved.

关键词： Molecular dynamics

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An Improved Unbiased Particle Filter

arXiv

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arXiv 2023年

作者： Jasra, Ajay Maama, Mohamed Ombao, Hernando 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 Statistics Program Computer Electrical and Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology Thuwal23955-6900 Saudi Arabia

In this paper we consider the filtering of partially observed multi-dimensional diffusion processes that are observed regularly at discrete times. We assume that, for numerical reasons, one has to time-discretize the diffusion process which typically leads to filtering that is subject to discretization bias. The approach in [16] establishes that when only having access to the time discretized diffusion it is possible to remove the discretization bias with an estimator of finite variance. We improve on the method in [16] by introducing a modified estimator based on the recent work of [17]. We show that this new estimator is unbiased and has finite variance. Moreover, we conjecture and verify in numerical simulations that substantial gains are obtained. That is, for a given mean square error (MSE) and a particular class of multi-dimensional diffusion, the cost to achieve the said MSE falls. Copyright © 2023, The Authors. All rights reserved.

关键词： Mean square error

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Optimal control, viscosity approximation and Arrhenius Law for the shallow lake problem

arXiv

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arXiv 2024年

作者： Koutsimpela, Angeliki Loulakis, Michail Department of Mathematics University of Augsburg Augsburg86159 Germany School of Applied Mathematical and Physical Sciences National Technical University of Athens Athens15780 Greece Institute of Applied and Computational Mathematics Foundation for Research and Technology Hellas Crete Heraklion70013 Greece

We prove existence of optimal control for the deterministic and stochastic shallow lake problem without any restrictions on the parameter space and we establish a generalization of the Arrhenius Law in the case of noise-dependent potentials, which naturally arise in control theory problems. We also prove a result about convergence of the derivatives in the viscosity approximation of the value function and use this result to derive the Arrhenius Law for the shallow lake *** Codes 93E20, 60H30, 49L25 Copyright © 2024, The Authors. All rights reserved.

关键词： Stochastic systems

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Empowering Optimal Control with Machine Learning: A Perspective from Model Predictive Control

arXiv

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arXiv 2022年

作者： Weinan, E. Han, Jiequn Long, Jihao AI for Science Institute Beijing China Center for Machine Learning Research School of Mathematical Sciences Peking University Beijing China Center for Computational Mathematics Flatiron Institute New York10010 United States Program of Applied and Computational Mathematics Princeton University Princeton08544 United States

Solving complex optimal control problems have confronted computational challenges for a long time. Recent advances in machine learning have provided us with new opportunities to address these challenges. This paper takes model predictive control, a popular optimal control method, as the primary example to survey recent progress that leverages machine learning techniques to empower optimal control solvers. We also discuss some of the main challenges encountered when applying machine learning to develop more robust optimal control algorithms. Copyright © 2022, The Authors. All rights reserved.

关键词： Machine learning

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The Effectiveness of the Finite Differences Method on Physical and Medical Images Based on a Heat Diffusion Equation 2

The Effectiveness of the Finite Differences Method on Physic...

引用

2nd International Virtual Conference on Pure Science, 2IVCPS 2021

作者： Rasheed, Mohammed Ali, Ali Hassan Alabdali, Osama Shihab, Suha Rashid, Ahmed Rashid, Taha Abed Hamad, Saad Hussein Applied Sciences Department University of Technology Baghdad Iraq Doctoral School of Mathematical and Computational Sciences University of Debrecen Pf. 400 DebrecenH-4002 Hungary Department of Mathematics College of Education for Pure Sciences University of Basrah Basrah Iraq College of Education for Pure Sciences University of Anbar Al-Anbar Iraq Al Iraqia University College of Arts Baghdad Iraq Skudai Johor Bahru81310 Malaysia College of Computer Science and Information Technology Al-Diwaniyah Iraq

In this paper, we study the influence of applying the well-known finite differences method on medical and physical images. These images will be used as coefficients in the steps of the solution after the images being imported and converted to arrays. The aim of the study is to show and analyze the changes that could happen to images for the sake of an enhancement. Experiments of one dimension and two dimensions will be illustrated by applying the explicit and the implicit methods using MATLAB to explain the way of how these methods affect images. Furthermore, we will study and measure the quality of the proposed images in each phase of the experiments using statistical metrics such as PSNR (Peak Signal to Noise Ratio), MSE (Mean Squared Error), MD (Maximum Difference) and some other statistical metrics. © Published under licence by IOP Publishing Ltd.

关键词： Finite difference method

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