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Universal subgradient and proximal bundle methods for convex and strongly convex hybrid composite optimization

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arXiv 2024年

作者： Guigues, Vincent Liang, Jiaming Monteiro, Renato D.C. School of Applied Mathematics FGV/EMAp Rio de Janeiro22250-900 Brazil Goergen Institute for Data Science Department of Computer Science University of Rochester RochesterNY14620 United States School of Industrial and Systems Engineering Georgia Institute of Technology AtlantaGA30332 United States

This paper develops two parameter-free methods for solving convex and strongly convex hybrid composite optimization problems, namely, a composite subgradient type method and a proximal bundle type method. Both functional and stationary complexity bounds for the two methods are established in terms of the unknown strong convexity parameter. To the best of our knowledge, the two proposed methods are the first universal methods for solving hybrid strongly convex composite optimization problems that do not rely on any restart scheme nor require the knowledge of the optimal value. © 2024, CC BY.

关键词： Optimization algorithms

Fine-Grained Synonymous Codon Usage Patterns and their Potential Role in Functional Protein Production

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Fine-Grained Synonymous Codon Usage Patterns and their Poten...

2021 IEEE International Conference on Bioinformatics and Biomedicine, BIBM 2021

作者： Babjac, Ashley Li, Jun Emrich, Scott University of Tennessee Department of Electrical Engineering and Computer Science KnoxvilleTN37996 United States University of Notre Dame Department of Applied and Computational Mathematics and Statistics Notre DameIN46556 United States

ISBN: (纸本)9781665401265

Multiple computational models exist that leverage the idea that some codons are 'preferred' to others when producing functional proteins. In this work, we aim to address the following two questions: (i) do proteins have similar codon usage subprofiles?, (ii) if so, can they be associated to specific Gene Ontology (GO) terms? To answer these questions, we analyze two different data sets E. coli and S. cerevisiae (yeast). For both, we use codon usage profiles that have been linked to protein co-translational folding and perform unsupervised clustering. Significantly, our clusters determine biologically meaningful patterns consistent with previously published observations. Our results suggest that codon patterns have potential to be incorporated into more complex deep learning-inspired frameworks in future work to better understand and predict functional protein production in a cell. © 2021 IEEE.

关键词： Proteins

Automated Organ Segmentation in 3D Biomedical Images Using Dual-Path 3D Attention U-ResNet

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Automated Organ Segmentation in 3D Biomedical Images Using D...

Ubiquitous Computing and Intelligent Information Systems (ICUIS), International Conference on

作者： J. Bhavana Thushara Hameed Maheswari Maruthakutti R. Sivaraman Sellamuthu Palanisamy Vijayanand B. Jegajothi Department of CS & AI SR University College of Engineering and Technology University of Technology and Applied Sciences Nizwa Sultanate of Oman Department of Mathematics Dwaraka Doss Goverdhan Doss Vaishnav College Arumbakkam Chennai Tamil Nadu Department of Computer Science and Engineering Institution name and address: Government of Engineering Erode SRS Tech Solutions Chennai

ISBN: (数字)9798331529635

ISBN: (纸本)9798331529642

Deep learning algorithms have made considerable strides in recent years, and these advancements have the potential to significantly improve multi-organ segmentation in three-dimensional biomedical images. This would result in improved diagnostic accuracy and efficiency in medical imaging. DA-TransUNet is an innovative architecture that successfully combines information on several scales and enhances feature extraction by utilizing the DA-Block encoder and the Convolutional Block Attention Module (CBAM). The assessed propsoed model using a variety of datasets, one of which being the LiTS dataset. Finally, were able to achieve a Dice coefficient of 92.56% and a Hausdorff Distance (HD95) of 28.09 mm for liver images. DA-TransUNet surpasses existing state-of-the-art segmentation models across a variety of medical imaging datasets, as demonstrated by the results of the experiments, which reveal considerable increases in accuracy and robustness. The discoveries that have obtained contribute to the advancement of automated segmentation approaches in medical imaging, which in turn facilitates increased diagnostic capabilities.

关键词： Image segmentation Three-dimensional displays Accuracy Biological system modeling Liver Biological systems Ubiquitous computing Robustness Biomedical imaging Resilience

Current-induced second harmonic generation of Dirac or Weyl semimetals in a strong magnetic field

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Physical Review B 2021年第4期103卷 L041301-L041301页

作者： Yang Gao Furu Zhang College of Computer Science and Engineering Anhui University of Science and Technology Huainan 232001 China Institute of Applied Physics and Computational Mathematics Beijing 100088 China

We theoretically investigate the second harmonic generation (SHG) of Dirac or Weyl semimetals under parallel DC electric and strong magnetic fields using the Boltzmann equation approach. The DC current-induced SHG process originates from the optical intraband transitions of the Landau subbands. It is a remarkable fingerprint of three-dimensional Dirac or Weyl dispersions and absent in other materials. An analytical formula for the SHG tensor is derived, and it shows chirality independence. The second-order nonlinear optical susceptibility is proportional to the DC field, giving strong optical nonlinearity up to 105pm/V with THz light, which is several orders larger than that of the usual materials. More interesting, the second harmonic conductivity is found to exhibit periodicity in magnetic field 1/B oscillations, which are similar to the Shubnikov–de Haas oscillations. Thus our work proposes another approach for SHG and potential applications of Dirac or Weyl semimetals in nonlinear optics.

关键词： Landau levels Nonlinear optical susceptibility Photoconductivity Semimetals Boltzmann theory Optical second-harmonic generation

Prescribing Decision Conservativeness in Two-Stage Power Markets: A Distributionally Robust End-to-End Approach

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Prescribing Decision Conservativeness in Two-Stage Power Mar...

Annual Conference on Information sciences and Systems (CISS)

作者： Zhirui Liang Qi Li Anqi Liu Yury Dvorkin Department of Electrical and Computer Engineering Johns Hopkins University Baltimore MD U.S. Department of Applied Mathematics and Statistics Johns Hopkins University Baltimore MD U.S. Department of Computer Science Johns Hopkins University Baltimore MD U.S. Department of Civil and System Engineering Johns Hopkins University Baltimore MD U.S.

ISBN: (数字)9798331513269

ISBN: (纸本)9798331513276

This paper presents an end-to-end framework for calibrating wind power forecast models to minimize operational costs in two-stage power markets, where the first stage involves a distributionally robust optimal power flow (DR-OPF) model. Unlike traditional methods that adjust forecast parameters and uncertainty quantification (UQ) separately, this framework jointly optimizes both the forecast model parameters and the decision conservativeness, which determines the size of the ambiguity set in the DR-OPF model. The framework aligns UQ with actual uncertainty realizations by directly optimizing downstream operational costs, a process referred to as cost-oriented calibration. The calibration is achieved using a gradient descent approach. To enable efficient differentiation, the DR-OPF problem is reformulated into a convex form, and the Envelope Theorem is leveraged to simplify gradient derivation in the two-stage setting. Additionally, the framework supports distributed implementation, effectively reducing computational overhead and enhancing efficiency. By proactively calibrating forecast parameters and prescribing optimal decision conservativeness, the framework significantly enhances cost efficiency and reliability in power system operations. Numerical experiments on an IEEE 5-bus system demonstrate the effectiveness and efficiency of the proposed approach.

关键词： Costs Uncertainty Predictive models Wind power generation Reliability theory Power markets Calibration Power system reliability Wind forecasting Load flow

Chebyshev Polynomial Broad Learning System

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Chebyshev Polynomial Broad Learning System

2021 International Conference on Information, Cybernetics, and Computational Social Systems, ICCSS 2021

作者： Feng, Shuang Wang, Bingshu Philip Chen, C.L. Beijing Normal University School of Applied Mathematics Zhuhai China Northwestern Polytechnical University School of Software Suzhou China South China University of Technology School of Computer Science and Engineering Guangzhou China

ISBN: (纸本)9781665402453

The broad learning system (BLS) has been attracting more and more attention due to its excellent property in the field of machine learning. A great deal of variants and hybrid structures of BLS have also been designed and developed for better performance in some specialized tasks. In this paper, the Chebyshev polynomials are introduced into the BLS to take advantage of their powerful approximation capability, where the feature windows are replaced by a set of Chebyshev polynomials. This new variant, named Chebyshev polynomial BLS (CPBLS), has a light structure with a reduction in computational complexity since the sparse autoencoder is removed. Instead, the dimension of each input sample is expended by n + 1 Chebyshev polynomials, mapping the original feature into a new feature space with higher dimension, which helps to classify the patterns in training. The proposed CPBLS is evaluated by some popular datasets from UCI and KEEL repositories, and it outperforms some representative neural networks and neuro-fuzzy models in terms of classification accuracy. The CPBLS also show some advantages over the recent developed compact fuzzy BLS (CFBLS) which indicates its great potential in future research and real-world applications. © 2021 IEEE.

关键词： Classification (of information)

WeatherQA: Can Multimodal Language Models Reason about Severe Weather?

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arXiv 2024年

作者： Ma, Chengqian Hua, Zhanxiang Anderson-Frey, Alexandra Iyer, Vikram Liu, Xin Qin, Lianhui Department of Applied Mathematics University of Washington United States Department of Atmospheric Sciences University of Washington United States Department of Computer Science and Engineering University of Washington United States University of California San Diego United States Allen Institute for Artificial Intelligence

Severe convective weather events, such as hail, tornadoes, and thunderstorms, often occur quickly yet cause significant damage, costing billions of dollars every year. This highlights the importance of forecasting severe weather threats hours in advance to better prepare meteorologists and residents in at-risk areas. Can modern large foundation models perform such forecasting? Existing weather benchmarks typically focus only on predicting time-series changes in certain weather parameters (e.g., temperature, moisture) with text-only features. In this work, we introduce WeatherQA, the first multimodal dataset designed for machines to reason about complex combinations of weather parameters (a.k.a., ingredients) and predict severe weather in real-world scenarios. The dataset includes over 8,000 (multiimages, text) pairs for diverse severe weather events. Each pair contains rich information crucial for forecasting-the images describe the ingredients capturing environmental instability, surface observations, and radar reflectivity, and the text contains in-depth forecast analyses written by human experts. With WeatherQA, we systematically evaluate state-of-the-art vision language models (VLMs), including GPT4, Claude3, Gemini-1.5, and a fine-tuned Llama3-based VLM, by designing two challenging tasks: (1) multi-choice QA for predicting affected area and (2) classification of the development potential of severe convection. These tasks require deep understanding of domain knowledge (e.g., atmospheric dynamics) and complex reasoning over multimodal data (e.g., interactions between weather parameters). We show a substantial gap between the strongest VLM, GPT4o, and human reasoning. Our comprehensive case study with meteorologists further reveals the weaknesses of the models, suggesting that better training and data integration are necessary to bridge this gap. WeatherQA is accessible through https://***/chengqianma/WeatherQA. © 2024, CC BY.

关键词： Data integration

Bayesian autoencoders for data-driven discovery of coordinates, governing equations and fundamental constants

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arXiv 2022年

作者： Gao, L. Mars Kutz, J. Nathan Paul G. Allen School of Computer Science & Engineering University of Washington SeattleWA United States Department of Applied Mathematics and Electrical and Computer Engineering University of Washington SeattleWA United States

Recent progress in autoencoder-based sparse identification of nonlinear dynamics (SINDy) under `1 constraints allows joint discoveries of governing equations and latent coordinate systems from spatio-temporal data, including simulated video frames. However, it is challenging for `1-based sparse inference to perform correct identification for real data due to the noisy measurements and often limited sample sizes. To address the data-driven discovery of physics in the low-data and high-noise regimes, we propose Bayesian SINDy autoencoders, which incorporate a hierarchical Bayesian sparsifying prior: Spike-and-slab Gaussian Lasso. Bayesian SINDy autoencoder enables the joint discovery of governing equations and coordinate systems with a theoretically guaranteed uncertainty estimate. To resolve the challenging computational tractability of the Bayesian hierarchical setting, we adapt an adaptive empirical Bayesian method with Stochatic gradient Langevin dynamics (SGLD) which gives a computationally tractable way of Bayesian posterior sampling within our framework. Bayesian SINDy autoencoder achieves better physics discovery with lower data and fewer training epochs, along with valid uncertainty quantification suggested by the experimental studies. The Bayesian SINDy autoencoder can be applied to real video data, with accurate physics discovery which correctly identifies the governing equation and provides a close estimate for standard physics constants like gravity g, for example, in videos of a pendulum. Copyright © 2022, The Authors. All rights reserved.

关键词： Dynamical systems

Information-Theoretically Private Matrix Multiplication From MDS-Coded Storage

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arXiv 2022年

作者： Zhu, Jinbao Li, Songze Li, Jie Guangzhou510006 China The Department of Computer Science and Engineering The Hong Kong University of Science and Technology Hong Kong The Hubei Key Laboratory of Applied Mathematics Faculty of Mathematics and Statistics Hubei University Wuhan430062 China

We study two problems of private matrix multiplication, over a distributed computing system consisting of a master node, and multiple servers that collectively store a family of public matrices using Maximum-Distance-Separable (MDS) codes. In the first problem of Private and Secure Matrix Multiplication (PSMM) from colluding servers, the master intends to compute the product of its confidential matrix A with a target matrix stored on the servers, without revealing any information about A and the index of target matrix to some colluding servers. In the second problem of Fully Private Matrix Multiplication (FPMM) from colluding servers, the matrix A is also selected from another family of public matrices stored at the servers in MDS form. In this case, the indices of the two target matrices should both be kept private from colluding servers. We develop novel strategies for the two PSMM and FPMM problems, which simultaneously guarantee information-theoretic data/index privacy and computation correctness. We compare the proposed PSMM strategy with a previous PSMM strategy with a weaker privacy guarantee (non-colluding servers), and demonstrate substantial improvements over the previous strategy in terms of communication and computation overheads. Moreover, compared with a baseline FPMM strategy that uses the idea of Private Information Retrieval (PIR) to directly retrieve the desired matrix multiplication, the proposed FPMM strategy significantly reduces storage overhead, but slightly incurs large communication and computation overheads. Copyright © 2022, The Authors. All rights reserved.

关键词： Matrix algebra