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Multilevel Monte Carlo for a class of Partially Observed Processes in Neuroscience

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arXiv 2023年

作者： Maama, Mohamed Jasra, Ajay Kamatani, Kengo 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 School of Data Science The Chinese University of Hong Kong CN Shenzhen China Institute of Statistical Mathematics Tokyo190-0014 Japan

In this paper we consider Bayesian parameter inference associated to a class of partially observed stochastic differential equations (SDE) driven by jump processes. Such type of models can be routinely found in applications, of which we focus upon the case of neuroscience. The data are assumed to be observed regularly in time and driven by the SDE model with unknown parameters. In practice the SDE may not have an analytically tractable solution and this leads naturally to a time-discretization. We adapt the multilevel Markov chain Monte Carlo method of [15], which works with a hierarchy of time discretizations and show empirically and theoretically that this is preferable to using one single time discretization. The improvement is in terms of the computational cost needed to obtain a pre-specified numerical error. Our approach is illustrated on models applied to examples of Bayesian inference problems using both simulated and real observed data from neuroscience. Copyright © 2023, The Authors. All rights reserved.

关键词： Stochastic systems

Multilevel Particle Filters for Partially Observed McKean-Vlasov Stochastic Differential Equations

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arXiv 2024年

作者： Awadelkarim, Elsiddig Jasra, Ajay 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 School of Data Science The Chinese University of Hong Kong Shenzhen China

In this paper we consider the filtering problem associated to partially observed McKean-Vlasov stochastic differential equations (SDEs). The model consists of data that are observed at regular and discrete times and the objective is to compute the conditional expectation of (functionals) of the solutions of the SDE at the current time. This problem, even the ordinary SDE case is challenging and requires numerical approximations. Based upon the ideas in [3, 12] we develop a new particle filter (PF) and multilevel particle filter (MLPF) to approximate the afore-mentioned expectations. We prove under assumptions that, for ϵ > 0, to obtain a mean square error of O(ϵ2) the PF has a cost per-observation time of O(ϵ−5) and the MLPF costs O(ϵ−4) (best case) or O(ϵ−4 log(ϵ)2) (worst case). Our theoretical results are supported by numerical experiments. © 2024, CC BY.

关键词： Mean square error

Particle-surface interactions in a uniform electric field

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arXiv 2022年

作者： Wang, Zhanwen Miksis, Michael J. Vlahovska, Petia M. Theoretical and Applied Mechanics Program Northwestern University EvanstonIL60208 United States Engineering Sciences and Applied Mathematics Northwestern University EvanstonIL60208 United States

The electrostatic force on a spherical particle near a planar surface is calculated for the cases of a uniform electric field applied in either normal or tangential direction to the surface. The particle and suspending media are assumed to be weakly conducting, so that that the leaky dielectric model applies. The Laplace equation for the electric potential is solved in bipolar coordinate system and the potential is obtained in terms of a series expansion of Legendre polynomials. The force on the particle is calculated using the Maxwell tensor. We find that in the case of normal electric field, which corresponds to a particle near an electrode, the force is always attractive but at a given separation it varies nontrivially with particle-suspending medium conductivity ratio;the force on a particle that is more conducting than the suspending medium is much larger compared to the force on a particle less conducing than the suspending medium. In the case of tangential electric field, which corresponds to a particle near an insulating boundary, the force is always repulsive. © 2022, CC BY-NC-ND.

关键词： Electric potential

Model-Based Assessment of Photoplethysmogram Signal Quality in Real-Life Environments

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Model-Based Assessment of Photoplethysmogram Signal Quality ...

European Signal Processing Conference (EUSIPCO)

作者： Yan-Wei Su Chia-Cheng Hao Gi-Ren Liu Yuan-Chung Sheu Hau-Tieng Wu Department of Applied Mathematics National Yang Ming Chiao Tung University Hsinchu Taiwan Data Science Degree Program National Taiwan University & Academia Sinica Taipei Taiwan Department of Mathematics National Cheng-Kung University Tainan Taiwan National Center for Theoretical Sciences Taipei Taiwan Courant Institute of Mathematical Sciences New York University New York NY USA

ISBN: (数字)9789464593617

ISBN: (纸本)9798331519773

Assessing signal quality is crucial for photoplethys-mogram analysis, yet a precise mathematical model for defining signal quality is often lacking, posing challenges in the quantitative analysis. To tackle this problem, we propose a Signal Quality Index (SQI) based on the adaptive non-harmonic model (ANHM) and a Signal Quality Assessment (SQA) model, which is trained using the boosting learning algorithm. The effectiveness of the proposed SQA model is tested on publicly available databases with experts' annotations. Result: The DaLiA database [20] is used to train the SQA model, which achieves favorable accuracy and macro- F1 scores in other public databases (accuracy 0.83, 0.76 and 0.87 and macro-F1 0.81, 0.75 and 0.87 for DaLiA-testing dataset, TROIKA dataset [32], and WESAD dataset [23], respectively). This preliminary result shows that the ANHM model and the model-based SQI have potential for establishing an interpretable SOA system.

关键词： Adaptation models Accuracy Databases Statistical analysis Signal processing algorithms Europe Signal processing Mathematical models Quality assessment Indexes

Global-Local Active Contour for Segmenting Images with Simultaneous Inhomogeneity and Texture

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SSRN

SSRN 2024年

作者： Shao, Pei-Chiang Department of Applied Mathematics Chung Yuan Christian University Zhongli District Taoyuan City320314 Taiwan Undergraduate Program in College of Electrical Engineering and Computer Science Chung Yuan Christian University Zhongli District Taoyuan City320314 Taiwan

Severe intensity inhomogeneity (InH) and complex real-world textures cause great difficulties and become two important issues in image segmentation and object extraction applications. Plenty of methods are proposed to tackle these issues, however, they usually perform poorly on images possess both InH and texture. In this paper, we propose a region-based active contour model for segmenting images with simultaneous inhomogeneity and texture. A new bias field possesses both global and local smoothness properties is proposed to handle the InH issue, and a pixel inhomogeneity factor (PIF) is employed to jointly deal with InH and textured images. We also employ the total variation (TV) regularization to further smooth and denoise the transformed PIF image, making the segmentation process to have the nice properties of global convergence and independence of contour initialization. A large number of numerical experiments and comparisons are conducted to demonstrate the effective performance of the newly proposed method. © 2024, The Authors. All rights reserved.

关键词： Textures

Perturbational Complexity by Distribution Mismatch: A Systematic Analysis of Reinforcement Learning in Reproducing Kernel Hilbert Space

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arXiv 2021年

作者： Long, Jihao Han, Jiequn Program of Applied and Computational Mathematics Princeton University United States Center for Computational Mathematics Flatiron Institute United States

Most existing theoretical analysis of reinforcement learning (RL) is limited to the tabular setting or linear models due to the difficulty in dealing with function approximation in high dimensional space with an uncertain environment. This work offers a fresh perspective into this challenge by analyzing RL in a general reproducing kernel Hilbert space (RKHS). We consider a family of Markov decision processes M of which the reward functions lie in the unit ball of an RKHS and transition probabilities lie in a given arbitrary set. We define a quantity called perturbational complexity by distribution mismatch ∆M(ǫ) to characterize the complexity of the admissible state-action distribution space in response to a perturbation in the RKHS with scale ǫ. We show that ∆M(ǫ) gives both the lower bound of the error of all possible algorithms and the upper bound of two specific algorithms (fitted reward and fitted Q-iteration) for the RL problem. Hence, the decay of ∆M(ǫ) with respect to ǫ measures the difficulty of the RL problem on M. We further provide some concrete examples and discuss whether ∆M(ǫ) decays fast or not in these examples. As a byproduct, we show that when the reward functions lie in a high dimensional RKHS, even if the transition probability is known and the action space is finite, it is still possible for RL problems to suffer from the curse of dimensionality. Copyright © 2021, The Authors. All rights reserved.

关键词： Iterative methods

Entropic Optimal Transport Eigenmaps for Nonlinear Alignment and Joint Embedding of High-Dimensional Datasets

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arXiv 2024年

作者： Landa, Boris Kluger, Yuval Ma, Rong Department of Electrical Engineering Yale University United States Program in Applied Mathematics Yale University United States Department of Biostatistics Harvard University United States Interdepartmental Program in Computational Biology and Bioinformatics Yale University United States Department of Pathology Yale University School of Medicine United States

Embedding high-dimensional data into a low-dimensional space is an indispensable component of data analysis. In numerous applications, it is necessary to align and jointly embed multiple datasets from different studies or experimental conditions. Such datasets may share underlying structures of interest but exhibit individual distortions, resulting in misaligned embeddings using traditional techniques. In this work, we propose Entropic Optimal Transport (EOT) eigenmaps, a principled approach for aligning and jointly embedding a pair of datasets with theoretical guarantees. Our approach leverages the leading singular vectors of the EOT plan matrix between two datasets to extract their shared underlying structure and align the datasets accordingly in a common embedding space. We interpret our approach as an inter-data variant of the classical Laplacian eigenmaps and diffusion maps embeddings, showing that it enjoys many favorable analogous properties. We then analyze a data-generative model where two observed high-dimensional datasets share latent variables on a common low-dimensional manifold, but each dataset is subject to data-specific translation, scaling, nuisance structures, and noise. We show that in a high-dimensional asymptotic regime, the EOT plan recovers the shared manifold structure by approximating a kernel function evaluated at the locations of the latent variables. Subsequently, we provide a geometric interpretation of our embedding by relating it to the eigenfunctions of population-level operators encoding the density and geometry of the shared manifold. Finally, we showcase the performance of our approach for data integration and embedding through simulations and analyses of real-world biological data, demonstrating its advantages over alternative methods in challenging scenarios. Copyright © 2024, The Authors. All rights reserved.

关键词： Embeddings

The total phenolic and flavonoid contents of Aloe vera and Morinda citrifolia extracts as antibacterial material against Pseudomonas aeruginosa

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Materials Today: Proceedings 2023年 72卷 2796-2802页

作者： Royani, Ahmad Hanafi, Muhammad Julistiono, Heddy Manaf, Azwar Postgraduate Program of Materials Science Study Department of Physics Faculty of Mathematics and Natural Sciences Universitas Indonesia Depok 16424 Indonesia Research Center for Metallurgy National Research and Innovation Agency Puspiptek Area Tangerang Selatan 15314 Indonesia Research Center for Raw Material of Medicine and Traditional Medicine National Research and Innovation Agency Puspiptek Area Tangerang Selatan 15314 Indonesia Research Center for Applied Microbiology National Research and Innovation Agency Jl. Raya Bogor Km. 46 Cibinong Science Center Cibinong 16911 Indonesia

Pseudomonas aeruginosa is a pioneer bacterium initiating the biofilm formation process so that it is corrosive to some metals in the marine environment. One of the efforts to prevent and control corrosion due to environmentally friendly biofilms is using green biocides. The extraction of Aloe vera and Morinda citrifolia with methanol were carried out to obtain antibacterial material. The extract of those plants with multilevel maceration method. The study aimed to identify the total phenolic and flavonoid contents in A. vera and M. citrifolia crude extracts and compare the two antibacterial extract activities. The total phenolic and flavonoid contents were analyzed using the Folin-Ciocalteu and the aluminum chloride colorimetric methods. The antibacterial activity against P. aeruginosa was conducted using the microdilution method to determine the minimum inhibitory concentration (MIC). The structure of the bioactive components of both A. vera and M. citrifolia extracts were identified using a liquid chromatography-mass spectrometer (LC/MS-MS). The MIC of A. vera and M. citrifolia for P. aeruginosa bacteria is about 6144 µg/mL, while the MIC of antibiotic Enrofloxacin is 16 µg/mL. The mean of total phenolic and flavonoid contents for the methanolic extracts of A. vera and M. citrifolia were 1.39% and 4.03% (phenolic), and 0.26% and 0.28% (flavonoids), respectively. The chemical structure of A. vera consists of 2″-O-Feruloylaloesin, Kaempferol-3-O-rutinoside, and Natsudaidain. At the same time, the chemical structure of M. citrifolia consists of 7-Hydroxy-Methoxycoumarin and Cirsiumaldehyde. A. vera and M. citrifolia crude extracts had lower inhibition than antibacterial control (Enrofloxacin) for P. aeruginosa. The lower bacteria inhibition was due to the low active materials (phenolic and flavonoid contents). So, the purification methods of crude extracts to obtain active materials with high antibacterial activity were needed. © 2022

关键词： Bacteria

Recent Advances and Applications of Machine Learning in Experimental Solid Mechanics: A Review

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arXiv 2023年

作者： Jin, Hanxun Zhang, Enrui Espinosa, Horacio D. Department of Mechanical Engineering Northwestern University EvanstonIL60208 United States Theoretical and Applied Mechanics Program Northwestern University EvanstonIL60208 United States Division of Applied Mathematics Brown University ProvidenceRI02912 United States

For many decades, experimental solid mechanics has played a crucial role in characterizing and understanding the mechanical properties of natural and novel materials. Recent advances in machine learning (ML) provide new opportunities for the field, including experimental design, data analysis, uncertainty quantification, and inverse problems. As the number of papers published in recent years in this emerging field is exploding, it is timely to conduct a comprehensive and up-to-date review of recent ML applications in experimental solid mechanics. Here, we first provide an overview of common ML algorithms and terminologies that are pertinent to this review, with emphasis placed on physics-informed and physics-based ML methods. Then, we provide thorough coverage of recent ML applications in traditional and emerging areas of experimental mechanics, including fracture mechanics, biomechanics, nano- and micro-mechanics, architected materials, and 2D material. Finally, we highlight some current challenges of applying ML to multi-modality and multi-fidelity experimental datasets and propose several future research directions. This review aims to provide valuable insights into the use of ML methods as well as a variety of examples for researchers in solid mechanics to integrate into their experiments. © 2023, CC BY.

关键词： Machine learning