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CONVERGENCE SPEED AND APPROXIMATION ACCURACY OF NUMERICAL MCMC

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arXiv 2022年

作者： Cui, Tiangang Dong, Jing Jasra, Ajay Tong, Xin T. School of Mathematics Monash University Australia Graduate School of Business Columbia University United States Applied Mathematics and Computational Science Program Computer Electrical Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology Saudi Arabia Department of Mathematics National University of Singapore Singapore

When implementing Markov Chain Monte Carlo (MCMC) algorithms, perturbation caused by numerical errors is sometimes inevitable. This paper studies how perturbation of MCMC affects the convergence speed and Monte Carlo estimation accuracy. Our results show that when the original Markov chain converges to stationarity fast enough and the perturbed transition kernel is a good approximation to the original transition kernel, the corresponding perturbed sampler has similar convergence speed and high approximation accuracy as well. We discuss two different analysis frameworks: ergodicity and spectral gap, both are widely used in the literature. Our results can be easily extended to obtain non-asymptotic error bounds for MCMC estimators. We also demonstrate how to apply our convergence and approximation results to the analysis of specific sampling algorithms, including Random walk Metropolis and Metropolis adjusted Langevin algorithm with perturbed target densities, and parallel tempering Monte Carlo with perturbed densities. Finally we present some simple numerical examples to verify our theoretical claims. Copyright © 2022, The Authors. All rights reserved.

关键词： Inverse problems

A BCLC Staging System for Hepatocellular Carcinoma using Swin Transformer and CT Imaging

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A BCLC Staging System for Hepatocellular Carcinoma using Swi...

Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC)

作者： Shun-Cheng Chang Pochuang Wang Weichung Wang Tung-Hung Su Jia-Horng Kao Che Lin Graduate Institute of Communication Engineering National Taiwan University (NTU) Taipei Taiwan Department of Computer Science and Information Engineering NTU Taipei Taiwan NTU Institute of Applied Mathematical Sciences Taipei Taiwan Department of Internal Medicine Division of Gastroenterology and Hepatology National Taiwan University Hospital Taipei Taiwan Department of Electrical Engineering NTU Taipei Taiwan NTU Center for Advanced Computing and Imaging in Biomedicine Taipei Taiwan NTU Smart Medicine and Health Informatics Program Taipei Taiwan

ISBN: (数字)9798350371499

ISBN: (纸本)9798350371505

The Barcelona Clinic Liver Cancer (BCLC) staging system plays a crucial role in clinical planning, offering valuable insights for effectively managing hepatocellular carcinoma. Accurate prediction of BCLC stages can significantly ease the workload on radiologists. However, few datasets are explicitly designed for discerning BCLC stages. Despite the common practice of appending BCLC labels to clinical data within datasets, the inherent imbalance in BCLC distribution is further amplified by the diverse purposes for which datasets are curated. In this study, we aim to develop a BCLC staging system using the advanced Swin Transformer model. Additionally, we explore the integration of two datasets, each originally intended for separate objectives, highlighting the critical challenge of preserving class distribution in practical study designs. This exploration is pivotal for ensuring the applicability of our developed staging system in the designed clinical settings. Our resulting BCLC staging system demonstrates an accuracy of 55.81% (±7.8%), contributing to advancing medical image-based research for predicting BCLC stages.

关键词： Liver cancer Accuracy Computed tomography Biological system modeling Transformers Planning Biomedical imaging

ReViT: A Hybrid Approach for BCLC Staging of Hepatocellular Carcinoma Using 3D CT with Multiple Instance Learning

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ReViT: A Hybrid Approach for BCLC Staging of Hepatocellular ...

IEEE EMBS International Conference on Information Technology Applications in Biomedicine (ITAB)

作者： Shun-Cheng Chang Hsin-Pei Yu Yi-Hsien Hsieh Pochuang Wang Weichung Wang Tung-Hung Su Jia-Horng Kao Che Lin Graduate Institute of Communication Engineering National Taiwan University (NTU) Taipei Taiwan Department of Computer Science and Information Engineering NTU Taipei Taiwan Institute of Applied Mathematical Sciences NTU Taipei Taiwan Department of Internal Medicine Division of Gastroenterology and Hepatology National Taiwan University Hospital Taipei Taiwan Department of Electrical Engineering NTU Taipei Taiwan Center for Advanced Computing and Imaging in Biomedicine NTU Taipei Taiwan Smart Medicine and Health Informatics Program NTU Taipei Taiwan

ISBN: (数字)9798350351552

ISBN: (纸本)9798350351569

Deep learning has revolutionized medical imaging, offering advanced methods for accurate diagnosis and treatment planning. The BCLC staging system is crucial for staging Hepatocellular Carcinoma (HCC), a high-mortality cancer. An automated BCLC staging system could significantly enhance diagnosis and treatment planning efficiency. However, we found that BCLC staging, which is directly related to the size and number of liver tumors, aligns well with the principles of the Multiple Instance Learning (MIL) framework. To effectively achieve this, we proposed a new preprocessing technique called Masked Cropping and Padding(MCP), which addresses the variability in liver volumes and ensures consistent input sizes. This technique preserves the structural integrity of the liver, facilitating more effective learning. Furthermore, we introduced Re ViT, a novel hybrid model that integrates the local feature extraction capabilities of Convolutional Neural Networks (CNNs) with the global context modeling of Vision Transformers (ViTs). Re ViT leverages the strengths of both architectures within the MIL framework, enabling a robust and accurate approach for BCLC staging. We will further explore the trade-off between performance and interpretability by employing TopK Pooling strategies, as our model focuses on the most informative instances within each bag.

关键词： Visualization Accuracy Three-dimensional displays Liver Transformers Planning Convolutional neural networks Context modeling Biomedical imaging Tumors

A micromirror array with annular partitioning for high-speed random-access axial focusing

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Light(Science & Applications) 2020年第1期9卷 241-255页

作者： Nathan Tessema Ersumo Cem Yalcin Nick Antipa Nicolas Pegard Laura Waller Daniel Lopez Rikky Muller The University of California Berkeley and University of CaliforniaSan Francisco Graduate Program in BioengineeringBerkeleyCA 94720USA Department of Electrical Engineering&Computer Sciences University of CaliforniaBerkeleyCA 94720USA Department of Applied Physical Sciences University of North Carolina at Chapel HillChapel HillNC 27514USA Chan Zuckerberg Biohub San FranciscoCA 94158USA Physical Measurement Laboratory National Institute of Standards and TechnologyGaithersburgMD 20899USA

Dynamic axial focusing functionality has recently experienced widespread incorporation in microscopy,augmented/virtual reality(AR/VR),adaptive optics and material ***,the limitations of existing varifocal tools continue to beset the performance capabilities and operating overhead of the optical systems that mobilize such *** varifocal tools that are the least burdensome to operate(*** crystal,elastomeric or optofluidic lenses)suffer from low(≈100 Hz)refresh ***,the fastest devices sacrifice either critical capabilities such as their dwelling capacity(*** gradient lenses or monolithic micromechanical mirrors)or low operating overhead(*** mirrors).Here,we present a general-purpose random-access axial focusing device that bridges these previously conflicting features of high speed,dwelling capacity and lightweight drive by employing lowrigidity micromirrors that exploit the robustness of defocusing phase ***,the device consists of an 8.2mm diameter array of piston-motion and 48-μm-pitch micromirror pixels that provide 2πphase shifting for wavelengths shorter than 1100 nm with 10-90% settling in 64.8μs(i.e.,15.44 kHz refresh rate).The pixels are electrically partitioned into 32 rings for a driving scheme that enables phase-wrapped operation with circular symmetry and requires<30 V per *** experiments demonstrated the array’s wide focusing range with a measured ability to target 29 distinct resolvable depth ***,the features of the proposed array offer the potential for compact,straightforward methods of tackling bottlenecked applications,including high-throughput single-cell targeting in neurobiology and the delivery of dense 3D visual information in AR/VR.

关键词： mirror axial random

Deep-Strong Coupling between Cavity Photons and Terahertz TO Phonons in PbTe

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Deep-Strong Coupling between Cavity Photons and Terahertz TO...

2023 Conference on Lasers and Electro-Optics, CLEO 2023

作者： Baydin, Andrey Manjappa, Manukumara Mishra, Sobhan Subhra Xu, Hongjing Tay, Fuyang Kim, Dasom Hernandez, Felix G.G. Rappl, Paulo H.O. Abramof, Eduardo Singh, Ranjan Kono, Junichiro Department of Electrical and Computer Engineering Rice University HoustonTX77005 United States Smalley-Curl Institute Rice University HoustonTX77005 United States Instrumentation and Applied Physics Department Indian Institute of Science Bangalore560012 India Center for Disruptive Photonic Technologies The Photonics Institute Nanyang Technological University 639798 Singapore Department of Physics and Astronomy Rice University HoustonTX77005 United States Applied Physics Graduate Program Smalley-Curl Institute Rice University HoustonTX77005 United States Instituto de Física Universidade de Sao Paulo SP Sao Paulo05508-090 Brazil Laboratorio Associado de Sensores e Materiais Instituto Nacional de Pesquisas Espaciais SP Sao Jose dos Campos12201-970 Brazil Division of Physics and Applied Physics School of Physical and Mathematical Sciences Nanyang Technological University 637371 Singapore Department of Material Science and NanoEngineering Rice University HoustonTX77005 United States

We have investigated the resonant coupling of photons with TO phonons in lead telluride in small-mode-volume terahertz cavities, observing a giant vacuum Rabi splitting on the order of the bare cavity-phonon frequency... 详细信息

ISBN: (纸本)9781957171258

关键词： Photons

EllipsoNet: Deep-learning-enabled optical ellipsometry for complex thin films

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arXiv 2022年

作者： Wang, Ziyang Lin, Yuxuan Cosmi Zhang, Kunyan Wu, Wenjing Huang, Shengxi Department of Electrical and Computer Engineering Rice University HoustonTX77005 United States Department of Electrical Engineering and Computer Sciences University of California BerkeleyCA94720 United States Department of Electrical Engineering The Pennsylvania State University University ParkPA16802 United States Applied Physics Graduate Program Smalley-Curl Institute Rice University HoustonTX77005 United States

Optical spectroscopy is indispensable for research and development in nanoscience and nanotechnology, microelectronics, energy, and advanced manufacturing. Advanced optical spectroscopy tools often require both specifically designed high-end instrumentation and intricate data analysis techniques. Beyond the common analytical tools, deep learning methods are well suited for interpreting high-dimensional and complicated spectroscopy data. They offer great opportunities to extract subtle and deep information about optical properties of materials with simpler optical setups, which would otherwise require sophisticated instrumentation. In this work, we propose a computational ellipsometry approach based on a conventional tabletop optical microscope and a deep learning model called EllipsoNet. Without any prior knowledge about the multilayer substrates, EllipsoNet can predict the complex refractive indices of thin films on top of these nontrivial substrates from experimentally measured optical reflectance spectra with high accuracies. This task was not feasible previously with traditional reflectometry or ellipsometry methods. Fundamental physical principles, such as the Kramers-Kronig relations, are spontaneously learned by the model without any further training. This approach enables in-operando optical characterization of functional materials within complex photonic structures or optoelectronic devices. © 2022, CC BY.

关键词： Refractive index

Direct Visualization of a Disorder Driven Electronic Smectic Phase in Dirac Nodal Line Semimetal GdSbTe

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arXiv 2024年

作者： Venkatesan, Balaji Guan, Syu-You Chang, Jen-Te Chiu, Shiang-Bin Yang, Po-Yuan Su, Chih-Chuan Chang, Tay-Rong Raju, Kalaivanan Sankar, Raman Fongchaiya, Somboon Chu, Ming-Wen Chang, Chia-Seng Chang, Guoqing Lin, Hsin Del Maestro, Adrian Kao, Ying-Jer Chuang, Tien-Ming Department of Physics National Taiwan University Taipei10617 Taiwan Nano Science and Technology Program Taiwan International Graduate Program Academia Sinica National Taiwan University Taipei11529 Taiwan Institute of Physics Academia Sinica Taipei11529 Taiwan Department of Physics National Cheng-Kung University Tainan701 Taiwan Center for Condensed Matter Sciences National Taiwan University Taipei10617 Taiwan Molecular Science and Technology Program Taiwan International Graduate Program Academia Sinica Taipei11529 Taiwan Division of Physics and Applied Physics School of Physical and Mathematical Sciences Nanyang Technological University 21 Nanyang Link 637371 Singapore Department of Physics and Astronomy University of Tennessee KnoxvilleTN37996 United States Institute for Advanced Materials & Manufacturing University of Tennessee KnoxvilleTN37996 United States Min H. Kao Department of Electrical Engineering and Computer Science University of Tennessee KnoxvilleTN37996 United States Center for Quantum Science and Technology National Taiwan University Taipei10607 Taiwan

Electronic liquid crystal (ELC) phases are spontaneous symmetry breaking states believed to arise from strong electron correlation in quantum materials such as cuprates and iron pnictides. Here, we report a direct observation of a smectic phase in a weakly correlated Dirac nodal line (DNL) semimetal GdSbxTe2-x. Incommensurate smectic charge modulation and intense local unidirectional nanostructure are visualized by using spectroscopic imaging - scanning tunneling microscopy. As topological materials with symmetry protected Dirac or Weyl fermions are mostly weakly correlated, the discovery of such an ELC phase are anomalous and raise questions on the origin of their emergence. Specifically, we demonstrate how chemical substitution generates these symmetry breaking phases before the system undergoes a charge density wave (CDW) - orthorhombic structural transition. Our results highlight the importance of impurities in realizing ELC phases and present a new material platform for exploring the interplay among quenched disorder, topology and electron correlation. Copyright © 2024, The Authors. All rights reserved.

关键词： Charge density waves

Learning Vector Quantized Shape Code for Amodal Blastomere Instance Segmentation

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Learning Vector Quantized Shape Code for Amodal Blastomere I...

IEEE International Symposium on Biomedical Imaging

作者： Won-Dong Jang Donglai Wei Xingxuan Zhang Brian Leahy Helen Yang James Tompkin Dalit Ben-Yosef Daniel Needleman Hanspeter Pfister School of Engineering and Applied Sciences Harvard University MA USA Boston College MA USA Department of Molecular and Cellular Biology Harvard University MA USA Harvard Graduate Program in Biophysics Harvard University MA USA Department of Computer Science Brown University RI USA Tel Aviv Sourasky Medical Center Fertility & IVF Institute Israel Dept. of Cell and Developmental Biology Sagol School of Neuroscience Tel Aviv University Israel

Blastomere instance segmentation is important for analyzing embryos’ abnormality. To measure the accurate shapes and sizes of blastomeres, their amodal segmentation is necessary. Amodal instance segmentation aims to recover an object’s complete silhouette even when the object is not fully visible. For each detected object, previous methods directly regress the target mask from input features. However, images of an object under different amounts of occlusion should have the same amodal mask output, making it harder to train the regression model. To alleviate the problem, we propose to classify input features into intermediate shape codes and recover complete object shapes. First, we pre-train the Vector Quantized Variational Autoencoder (VQ-VAE) model to learn these discrete shape codes from ground truth amodal masks. Then, we incorporate the VQ-VAE model into the amodal instance segmentation pipeline with an additional refinement module. We also detect an occlusion map to integrate occlusion information with a backbone feature. As such, our network faithfully detects bounding boxes of amodal objects. On an internal embryo cell image benchmark, the proposed method outperforms previous state-of-the-art methods. To show generalizability, we show segmentation results on the public KINS natural image benchmark. Our method would enable accurate measurement of blastomeres in In Vitro Fertilization (IVF) clinics, potentially increasing the IVF success rate.

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PHYSICS INFORMED MACHINE LEARNING WITH SMOOTHED PARTICLE HYDRODYNAMICS: HIERARCHY OF REDUCED LAGRANGIAN MODELS OF TURBULENCE

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arXiv 2021年

作者： Woodward, Michael Tian, Yifeng Hyett, Criston Fryer, Chris Stepanov, Mikhail Livescu, Daniel Chertkov, Michael Graduate Interdisciplinary Program in Applied Mathematics UArizona TucsonAZ85721 United States Department of Mathematics UArizona TucsonAZ85721 United States Computer Computational and Statistical Sciences Division LANL Los AlamosNM87544 United States

Building efficient, accurate and generalizable reduced order models of developed turbulence remains a major challenge. This manuscript approaches this problem by developing a hierarchy of parameterized reduced Lagrangian models for turbulent flows, and investigates the effects of enforcing physical structure through Smoothed Particle Hydrodynamics (SPH) versus relying on neural networks (NN)s as universal function approximators. Starting from Neural Network (NN) parameterizations of a Lagrangian acceleration operator, this hierarchy of models gradually incorporates a weakly compressible and parameterized SPH framework, which enforces physical symmetries, such as Galilean, rotational and translational invariances. Within this hierarchy, two new parameterized smoothing kernels are developed in order to increase the flexibility of the learn-able SPH simulators. For each model we experiment with different loss functions which are minimized using gradient based optimization, where efficient computations of gradients are obtained by using Automatic Differentiation (AD) and Sensitivity Analysis (SA). Each model within the hierarchy is trained on two data sets associated with weekly compressible Homogeneous Isotropic Turbulence (HIT): (1) a validation set using weakly compressible SPH;and (2) a high fidelity set from Direct Numerical Simulations (DNS). Numerical evidence shows that encoding more SPH structure improves generalizability to different turbulent Mach numbers and time shifts, and that including the novel parameterized smoothing kernels improves the accuracy of SPH at the resolved scales. Copyright © 2021, The Authors. All rights reserved.

关键词： Parameterization