检索结果-内蒙古大学图书馆

A Flow Artist for High-Dimensional Cellular Data

学校读者我要写书评

暂无评论

A Flow Artist for High-Dimensional Cellular Data

IEEE Workshop on Machine Learning for Signal Processing

作者： Kincaid MacDonald Dhananjay Bhaskar Guy Thampakkul Nhi Nguyen Joia Zhang Michael Perlmutter Ian Adelstein Smita Krishnaswamy Department of Mathematics Yale University Department of Genetics Yale School of Medicine Department of Computer Science Yale University Department of Mathematics Pomona College Applied Mathematics Program Yale University Department of Statistics University of Washington Department of Mathematics Boise State University Computational Biology and Bioinformatics Program Yale University

We consider the problem of embedding point cloud data sampled from an underlying manifold with an associated flow or velocity. Such data arises in many contexts where static snapshots of dynamic entities are measured, including in high-throughput biology such as single-cell transcriptomics. Existing embedding techniques either do not utilize velocity information or embed the coordinates and velocities independently, i.e., they either impose velocities on top of an existing point embedding or embed points within a prescribed vector field. Here we present FlowArtist, a neural network that embeds points while jointly learning a vector field around the points. The combination allows FlowArtist to better separate and visualize velocity-informed structures. Our results, on toy datasets and single-cell RNA velocity data, illustrate the value of utilizing coordinate and velocity information in tandem for embedding and visualizing high-dimensional data.

关键词：

A Nonlinear, Conservative, Entropic Fokker-Planck Model for Multi-Species Collisions

学校读者我要写书评

暂无评论

arXiv 2024年

作者： Habbershaw, Evan Hauck, Cory D. Hu, Jingwei Haack, Jeffrey R. Department of Mathematics The University of Tennessee KnoxvilleTN37996 United States Computer Science and Mathematics Division Oak Ridge National Laboratory Oak RidgeTN37831 United States Department of Applied Mathematics University of Washington SeattleWA98195 United States Computer Computational and Statistical Sciences Division Los Alamos National Laboratory Los AlamosNM87545 United States

A multi-species Fokker-Planck model for simulating particle collisions in a plasma is presented. The model includes various parameters that must be tuned. Under reasonable assumptions on these parameters, the model satisfies appropriate conservation laws, dissipates an entropy, and satisfies an H-Theorem. In addition, the model parameters provide the additional flexibility that is used to match simultaneously momentum and temperature relaxation formulas derived from the Boltzmann collision operator for a binary mixture with Coulomb potentials. A numerical method for solving the resulting space-homogeneous kinetic equation is presented and two examples are provided to demonstrate the relaxation of species bulk velocities and temperatures to their equilibrium values. © 2024, CC BY.

关键词： Numerical methods

Multilevel Monte Carlo Methods for the Grad-Shafranov Free Boundary Problem

学校读者我要写书评

暂无评论

SSRN

SSRN 2023年

作者： Elman, Howard C. Liang, Jiaxing Sánchez-Vizuet, Tonatiuh Department of Computer Science Institute for Advanced Computer Studies University of Maryland College Park United States Applied Mathematics & Statistics and Scientific Computing Program University of Maryland College Park United States Department of Mathematics The University of Arizona United States

The equilibrium configuration of a plasma in an axially symmetric reactor is described mathematically by a free boundary problem associated with the celebrated Grad-Shafranov equation. The presence of uncertainty in the model parameters introduces the need to quantify the variability in the predictions. This is often done by computing a large number of model solutions on a computational grid for an ensemble of parameter values and then obtaining estimates for the statistical properties of solutions. In this study, we explore the savings that can be obtained using multilevel Monte Carlo methods, which reduce costsby performing the bulk of the computations on a sequence of spatial grids that are coarser than the one that would typically be used for a simple Monte Carlo simulation. We examine this approach using both a set of uniformly refined grids and a set of adaptively refined grids guided by a discrete error estimator. Numerical experiments show that multilevel methods dramatically reduce the cost of simulation, with cost reductionstypically on the order of 60 or more and possibly as large as 200. Adaptive gridding results in more accurate computation of geometric quantities such as x-points associated with the model. © 2023, The Authors. All rights reserved.

关键词： Monte Carlo methods

Tackling the Curse of Dimensionality with Physics-Informed Neural Networks

学校读者我要写书评

暂无评论

arXiv 2023年

作者： Hu, Zheyuan Shukla, Khemraj Karniadakis, George Em Kawaguchi, Kenji Department of Computer Science School of Computing National University of Singapore Singapore119077 Singapore Division of Applied Mathematics Brown University ProvidenceRI02912 United States

The curse-of-dimensionality taxes computational resources heavily with exponentially increasing computational cost as the dimension increases. This poses great challenges in solving high-dimensional partial differential equations (PDEs), as Richard E. Bellman first pointed out over 60 years ago. While there has been some recent success in solving numerical PDEs in high dimensions, such computations are prohibitively expensive, and true scaling of general nonlinear PDEs to high dimensions has never been achieved. We develop a new method of scaling up physics-informed neural networks (PINNs) to solve arbitrary high-dimensional PDEs. The new method, called Stochastic Dimension Gradient Descent (SDGD), decomposes a gradient of PDEs’ and PINNs’ residual into pieces corresponding to different dimensions and randomly samples a subset of these dimensional pieces in each iteration of training PINNs. We prove theoretically the convergence and other desired properties of the proposed method. We demonstrate in various diverse tests that the proposed method can solve many notoriously hard high-dimensional PDEs, including the Hamilton-Jacobi-Bellman (HJB) and the Schrödinger equations in tens of thousands of dimensions very fast on a single GPU using the PINNs mesh-free approach. Notably, we solve nonlinear PDEs with nontrivial, anisotropic, and inseparable solutions in less than one hour for 1,000 dimensions and in 12 hours for 100,000 dimensions on a single GPU using SDGD with PINNs. Since SDGD is a general training methodology of PINNs, it can be applied to any current and future variants of PINNs to scale them up for arbitrary high-dimensional *** Codes 14J60 © 2023, CC BY.

关键词： Stochastic systems

Multilevel Monte Carlo methods for the Grad-Shafranov free boundary problem

学校读者我要写书评

暂无评论

arXiv 2023年

The equilibrium configuration of a plasma in an axially symmetric reactor is described mathematically by a free boundary problem associated with the celebrated Grad-Shafranov equation. The presence of uncertainty in the model parameters introduces the need to quantify the variability in the predictions. This is often done by computing a large number of model solutions on a computational grid for an ensemble of parameter values and then obtaining estimates for the statistical properties of solutions. In this study, we explore the savings that can be obtained using multilevel Monte Carlo methods, which reduce costs by performing the bulk of the computations on a sequence of spatial grids that are coarser than the one that would typically be used for a simple Monte Carlo simulation. We examine this approach using both a set of uniformly refined grids and a set of adaptively refined grids guided by a discrete error estimator. Numerical experiments show that multilevel methods dramatically reduce the cost of simulation, with cost reductions typically on the order of 60 or more and possibly as large as 200. Adaptive gridding results in more accurate computation of geometric quantities such as x-points associated with the *** Codes 65Z05, 65C05, 62P35, 35R35, 35R60 © 2023, CC BY.

关键词： Monte Carlo methods

Unsupervised Integration of Single-Cell Multi-omics Datasets with Disproportionate Cell-Type Representation 26th

学校读者我要写书评

暂无评论

Unsupervised Integration of Single-Cell Multi-omics Dataset...

26th International Conference on Research in Computational Molecular Biology, RECOMB 2022

作者： Demetçi, Pınar Santorella, Rebecca Sandstede, Björn Singh, Ritambhara Center for Computational Molecular Biology Brown University ProvidenceRI02912 United States Department of Computer Science Brown University ProvidenceRI02912 United States Division of Applied Mathematics Brown University ProvidenceRI02912 United States

ISBN: (纸本)9783031047480

Integrated analysis of multi-omics data allows the study of how different molecular views in the genome interact to regulate cellular processes;however, with a few exceptions, applying multiple sequencing assays on the same single cell is not possible. While recent unsupervised algorithms align single-cell multi-omic datasets, these methods have been primarily benchmarked on co-assay experiments rather than the more common single-cell experiments taken from separately sampled cell populations. Therefore, most existing methods perform subpar alignments on such datasets. Here, we improve our previous work Single Cell alignment using Optimal Transport (SCOT) by using unbalanced optimal transport to handle disproportionate cell-type representation and differing sample sizes across single-cell measurements. We show that our proposed method, SCOTv2, consistently yields quality alignments on five real-world single-cell datasets with varying cell-type proportions and is computationally tractable. Additionally, we extend SCOTv2 to integrate multiple (M≥ 2 ) single-cell measurements and present a self-tuning heuristic process to select hyperparameters in the absence of any orthogonal correspondence information. Available at: http://***/SCOT. © 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.

关键词： Data integration

Design of Drone Remote-Control System using Human Motion Recognition 5

学校读者我要写书评

暂无评论

Design of Drone Remote-Control System using Human Motion Rec...

5th IEEE Eurasian Conference on Educational Innovation, ECEI 2022

作者： Chen, Shyh-Wei Lai, Yu-Chun Liu, Chia-Hui Kuo, Chin-Guo Tunghai University Department of Computer Science Taichung Taiwan Tunghai University Master Program of Digital Innovation Taichung Taiwan Chinese Culture University Department of Applied Mathematics Taipei Taiwan National Taiwan Normal University Department of Industrial Education Taipei Taiwan

ISBN: (纸本)9781665433181

At present, the most common and low-cost method to control the drone is to use a mobile phone with an APP. The operator takes his mobile phone screen as a human-machine interface, and at the same time controls and receives the images returned by the drone. The control mode can be divided into two symmetry modes according to how the operator views and knows the location of the drone: exocentric viewing and egocentric viewing mode. In the exocentric viewing mode, the operator directly visually confirms the position of the drone, while in the egocentric viewing mode, the drone is equipped with a camera and transmits the flight image to the operator in real-time. Since the drone cannot be far away from the operator in the exocentric viewing mode, the relative egocentric mode allows the operator to feel immersed in the environment to control the drone more accurately. Therefore, by adapting the egocentric viewing and using human motion recognition, an unmanned vehicle remote-control system is designed. The low-speed, small-scaled, nature-stability UAVs are ideally suited for the proposed system. The system was designed with a PID controller to improve the UAV's handling. The experimental results verified the feasibility of the UVA control system and it could stabilize the posture of the drone. © 2022 IEEE.

关键词： Drones

Particle swarm optimization with local search for height-map surface reconstruction from point clouds in reverse engineering

学校读者我要写书评

暂无评论

Neural Computing and Applications 2024年 1-20页

作者： Gálvez, Akemi Fister, Iztok Deb, Suash Fister, Iztok Iglesias, Andrés Dept. of Applied Mathematics and Computational Sciences E.T.S.I. Caminos Canales y Puertos University of Cantabria Avda. de los Castros s/n Santander39005 Spain Faculty of Pharmaceutical Sciences Toho University 2-2-1 Miyama Funabashi274-8510 Japan Faculty of Electrical Engineering and Computer Science University of Maribor Koroska cesta 34 Maribor2000 Slovenia IT & Educational Consultant Ranchi India Distinguished Professorial Associate Decision Sciences and Modeling Program Victoria University Melbourne Australia

Surface reconstruction is a classical process in industrial engineering and manufacturing, particularly in reverse engineering, where the goal is to obtain a digital model from a physical object. For that purpose, the real object is typically scanned or digitized and the resulting point cloud is then fitted to mathematical surfaces through numerical optimization. The choice of the approximating functions is crucial for the accuracy of the process. Real-world objects such as manufactured workpieces often require complex nonlinear approximating functions, which are not well suited for standard numerical methods. In a previous paper presented at the ISMSI 2023 conference, we addressed this issue by using manually selected approximation functions via optimization through the cuckoo search algorithm with Lévy flights. Building upon that work, this paper presents an enhanced and extended method for surface reconstruction by using height-map surfaces obtained through a combination of exponential, polynomial and logarithmic functions. A feasible approach for this goal is to consider continuous bivariate distribution functions, which ensures consistent models along with good mathematical properties for the output shapes, such as smoothness and integrability. However, this approach leads to a difficult multivariate, constrained, multimodal continuous nonlinear optimization problem. To tackle this issue, we apply particle swarm optimization, a popular swarm intelligence technique for continuous optimization. The method is hybridized with a local search procedure for further improvement of the solutions and applied to a benchmark of 15 illustrative examples of point clouds fitted to different surface models. The performance of the method is analyzed through several computational experiments. The numerical and graphical results show that the method is able to recover the shape of the point clouds accurately and automatically. Furthermore, our approach outperforms other alternati

关键词： Particle swarm optimization (PSO)

Causal Discovery over High-Dimensional Structured Hypothesis Spaces with Causal Graph Partitioning

学校读者我要写书评

暂无评论

arXiv 2024年

作者： Shah, Ashka DePavia, Adela Hudson, Nathaniel Foster, Ian Stevens, Rick Department of Computer Science University of Chicago ChicagoIL United States Committee on Computational and Applied Mathematics University of Chicago ChicagoIL United States Data Science and Learning Division Argonne National Laboratory LemontIL United States

The aim in many sciences is to understand the mechanisms that underlie the observed distribution of variables, starting from a set of initial hypotheses. Causal discovery allows us to infer mechanisms as sets of cause and effect relationships in a generalized way-without necessarily tailoring to a specific domain. Causal discovery algorithms search over a structured hypothesis space, defined by the set of directed acyclic graphs, to find the graph that best explains the data. For high-dimensional problems, however, this search becomes intractable and scalable algorithms for causal discovery are needed to bridge the gap. In this paper, we define a novel causal graph partition that allows for divide-and-conquer causal discovery with theoretical guarantees. We leverage the idea of a superstructure-a set of learned or existing candidate hypotheses-to partition the search space. We prove under certain assumptions that learning with a causal graph partition always yields the Markov Equivalence Class of the true causal graph. We show our algorithm achieves comparable accuracy and a faster time to solution for biologically-tuned synthetic networks and networks up to 104 variables. This makes our method applicable to gene regulatory network inference and other domains with high-dimensional structured hypothesis spaces. © 2024, CC BY.

关键词：