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An equivalent reformulation and multi-proximity gradient algorithms for a class of nonsmooth fractional programming

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arXiv 2023年

作者： Zhou, Junpeng Zhang, Na Li, Qia School of Computer Sciences and Engineering Sun Yat-Sen University Guangzhou510006 China Department of Applied Mathematics College of Mathematics and Informatics South China Agricultural University Guangzhou510642 China School of Computer Sciences and Engineering Guangdong Province Key Laboratory of Computational Science Sun Yat-Sen University Guangzhou510006 China

In this paper, we consider a class of structured fractional programs, where the numerator part is the sum of a block-separable (possibly nonsmooth nonconvex) function and a locally Lipschitz differentiable (possibly nonconvex) function, while the denominator is a convex (possibly nonsmooth) function. We first present a novel reformulation for the original problem and show the relationship between optimal solutions, critical points and KL exponents of these two problems. Inspired by the reformulation, we propose a flexible framework of multi-proximity gradient algorithms (MPGA), which computes the proximity operator with respect to the Fenchel conjugate associated with the convex denominator of the original problem rather than evaluating its subgradient as in the existing methods. Also, MPGA employs a nonmonotone linear-search scheme in its gradient descent step, since the smooth part in the numerator of the original problem is not globally Lipschitz differentiable. Based on the framework of MPGA, we develop two specific algorithms, namely, cyclic MPGA and randomized MPGA, and establish their subsequential convergence under mild conditions. Moreover, the sequential convergence of cyclic MPGA with the monotone line-search (CMPGA ML) is guaranteed if the extended objective associated with the reformulated problem satisfies the Kurdyka-Lojasiewicz (KL) property and some other mild assumptions. In particular, we prove that the corresponding KL exponents are 12 for several special cases of the fractional programs, and so, CMPGA ML exhibits a linear convergence rate. Finally, some preliminary numerical experiments are performed to demonstrate the efficiency of our proposed algorithms. Copyright © 2023, The Authors. All rights reserved.

关键词： Gradient methods

PARAMETERIZED PROXIMAL-GRADIENT ALGORITHMS FOR L1/L2 SPARSE SIGNAL RECOVERY

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arXiv 2023年

作者： Zhang, Na Liu, Xinrui Li, Qia Department of Applied Mathematics College of Mathematics and Informatics South China Agricultural University Guangzhou510642 China School of Mathematics and Statistics Shandong Normal University Jinan250358 China Guangdong Province Key Laboratory of Computational Science School of Computer Science and Engineering Sun Yat-sen University Guangzhou510275 China

The ratio of 1 and 2 norms (1/2), serving as a sparse promoting function, receives considerable attentions recently due to its effectiveness for sparse signal recovery. In this paper, we propose an 1/2 based penalty model for recovering sparse signals from noiseless or noisy observations. It is proven that stationary points of the proposed problem tend to those of the elliptically constrained 1/2 minimization problem as the smoothing parameter goes to zero. Moreover, inspired by the parametric approach for the fractional programming, we design a parameterized proximal-gradient algorithm (PPGA) as well as its line search counterpart (PPGA_L) for solving the proposed model. The closed-form solution of the involved proximity operator is derived, which enable the efficiency of the proposed algorithms. We establish the global convergence of the entire sequences generated by PPGA and PPGA_L with monotone objective values by taking advantage of the fact that the objective of the proposed model is a KL function. Numerical experiments show the efficiency of the proposed algorithms over the state-of-the-art methods in both noiseless and noisy sparse signal recovery problems. Copyright © 2023, The Authors. All rights reserved.

关键词： Efficiency

Accelerated sound propagation simulations using an error-free Fourier method coupled with the spectral element method 51

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Accelerated sound propagation simulations using an error-fre...

51st International Congress and Exposition on Noise Control engineering, Internoise 2022

作者： Borrel-Jensen, Nikolas Engsig-Karup, Allan P. Hornikx, Maarten Jeong, Cheol-Ho Acoustic Technology Department of Electrical and Photonics Engineering Technical University of Denmark Kongens Lyngby2800 Denmark Department of Applied Mathematics and Computer Science Technical University of Denmark Kongens Lyngby2800 Denmark Department of the Built Environment Eindhoven University of Technology Eindhoven5612 AZ Netherlands

ISBN: (纸本)9781906913427

Simulating acoustics efficiently and accurately using numerical methods has been an active research area for the last decades and has applications in computer games, VR/AR, and architectural design. However, their extensive computation time makes these methods challenging for large scenes and broad frequency ranges. This work attempts to accelerate the simulations using rectangular decomposition, enabling error-free propagation in the bulk of the domain consisting of air. We exploit the analytical solution to the wave equation in rectangular domains calculated using the Fast Fourier Transform with near-optimal spatial discretization satisfying the Nyquist criterium. Coupling with the spectral element method near the boundaries results in a method capable of handling complex geometries with realistic boundaries, though with the caveat that additional errors and computational overhead may result from the interface. This paper will investigate the accuracy and efficiency of the proposed domain decomposition method compared to a spectral element implementation running in the entire domain and the results in 1D indicate an 18 times speedup factor for relative errors below 9%. © 2022 Internoise 2022 - 51st International Congress and Exposition on Noise Control engineering. All rights reserved.

关键词： Errors

Robust Texture Analysis via Optimal Mass Transport: Application to Medical Images Classification 8

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Robust Texture Analysis via Optimal Mass Transport: Applicat...

8th International Conference on engineering and Emerging Technologies, ICEET 2022

作者： Belkhatir, Zehor Iyer, Aditi Mathews, James C. Pouryahya, Maryam Nadeem, Saad Deasy, Joseph O. Apte, Aditya P. Tannenbaum, Allen R. De Montfort University School of Engineering and Sustainable Development Leicester United Kingdom Memorial Sloan Kettering Cancer Centre Depatment of Medical Physics New York United States Stony Brook University Departments of Computer Science Applied Mathematics and Statistics New York United States

ISBN: (纸本)9781665491068

The emerging field of radiomics, which consists of transforming standard-of-care images into quantifiable scalar statistics, endeavors to reveal the information hidden in these macroscopic images. This field of research has found different applications ranging from phenotyping and tumor classification to outcome prediction and treatment planning. Texture analysis, which often consists of reducing spatial texture matrices to summary scalar features, has been shown to be important in many of the later applications. However, as pointed out in many studies, some of the derived texture statistics are strongly correlated and tend to contribute redundant information;and are also sensitive to the parameters used in their computation, e.g., the number of gray intensity levels. In the present study, we propose new set of spatial texture features that consider texture matrices in general, with an emphasis here on gray-level co-occurrence matrix (GLCM), as non-parametric multivariate objects. The proposed modeling approach avoids evaluating redundant and strongly correlated features and also prevents the feature processing steps. Then, via the Wasserstein distance from optimal mass transport theory, we propose to compare these spatial objects to identify computerized tomography slices with dental artifacts in head and neck cancer. We demonstrate the robustness of the proposed classification approach with respect to the GLCM extraction parameters and the size of the training set. Comparisons with the random forest classifier, which is constructed on scalar texture features, demonstrate the efficiency and robustness of the proposed algorithm. © 2022 IEEE.

关键词： Textures

A Hierarchical Framework for Minimising Emissions in Hybrid Gas-Renewable Energy Systems Under Forecast Uncertainty

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SSRN

SSRN 2024年

作者： Hoang, Kiet Tuan Thilker, Christian Ankerstjerne Knudsen, Brage Rugstad Imsland, Lars Struen Norwegian University of Science and Technology Department of Engineering Cybernetics Trondheim7034 Norway Technical University of Denmark Compute Department of Applied Mathematics and Computer Science Kgs. LyngbyDK-2800 Denmark Department of Gas Technology SINTEF Energy Research Trondheim7034 Norway

Developing and deploying renewables in existing energy systems are pivotal in Europe's transition to net-zero emissions. In this transition, gas turbines (GTs) will be central for balancing purposes. However, a significant hurdle in minimising emissions of GTs operating in combination with intermittent renewables arises from the reliance on unreliable meteorological forecasts. Here, we propose a hierarchical framework for decoupling this operational problem into a balancing and emissions minimisation problem. Balancing is ensured with a high-level stochastic balancing filter (SBF) based on data-driven stochastic grey-box models for the uncertain intermittent renewable. The filter utilises probabilistic forecasting and less conservative chance constraints to compute safe bounds, within which a proposed low-level economic predictive controller further minimises emissions of the GTs during operations. As GTs exhibit semi-continuous operating regions, complementarity constraints are utilised to fully exploit each GT's allowed operational range. The proposed method is validated in simulation for a gas-balanced hybrid renewable system with batteries, three GTs with varying capacities, and a wind farm. Using real historical operational wind data, our simulation shows that the proposed framework balances the energy demand and minimises emissions with up to 4.35% compared with other conventional control strategies in simulation by minimising the GT emissions directly with complementarity constraints in the low-level controller and indirectly with less conservative chance constraints in the high-level filter. The simulations show that the computational cost of the proposed framework is well within requirements for real-time applications. Thus, the proposed operational framework enables increased renewable share in hybrid energy systems with GTs and renewable energy and subsequently contributes to de-carbonising these types of isolated or grid-connected systems onshore and off

关键词： Stochastic systems

Ambient- and high-pressure studies of structural, electronic, and magnetic properties of single-crystal EuZn2P2

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Physical Review B 2024年第1期110卷 014421-014421页

作者： Damian Rybicki Kamila Komędera Janusz Przewoźnik Łukasz Gondek Czesław Kapusta Karolina Podgórska Wojciech Tabiś Jan Żukrowski Lan Maria Tran Michał Babij Zbigniew Bukowski Ladislav Havela Volodymyr Buturlim Jiri Prchal Martin Divis Petr Kral Ilja Turek Itzhak Halevy Jiri Kastil Martin Misek Utpal Dutta Dominik Legut Faculty of Physics and Applied Computer Science al. A. Mickiewicza 30 30-059 Kraków Poland Mössbauer Spectroscopy Laboratory Faculty of Mathematics and Physics Department of Condensed Matter Physics Ke Karlovu 3 121 16 Prague 2 Czech Republic Unit of Nuclear Engineering Faculty of Engineering Science Na Slovance 1999/2 182 00 Prague 8 Czech Republic VŠB -

A thorough study of EuZn2P2 single crystals, which were grown from Sn flux, was performed using both bulk (heat capacity, ac susceptibility, dc magnetization, electrical resistivitivity, magnetoresistance) and microscopic (Mössbauer spectroscopy) techniques. Electrical resistance and magnetic susceptibility were measured also under high pressure conditions (up to 19 and 9.5 GPa, respectively). Further insight into electronic properties and phonons is provided by ab initio calculations. The results indicate that EuZn2P2 is an antiferromagnet with strong Eu-Eu exchange coupling of ferromagnetic type within the basal plane and weaker antiferromagnetic interaction along the c axis. The Eu magnetic moments are tilted from the basal plane. Hydrostatic pressure strongly affects both magnetic (increase of the Néel temperature) and electronic (suppression of the band gap and semimetallic behavior) properties, indicating a strong interplay of structure with magnetic and electronic degrees of freedom.

关键词： Antiferromagnetism Density of states Electronic structure of atoms & molecules First-principles calculations Antiferromagnets Rare-earth magnetic materials AC susceptibility measurements Crystal growth DC susceptibility measurements Magnetization measurements Mössbauer spectroscopy Pressure effects Pressure techniques Scanning electron microscopy Tight-binding model X-ray diffraction

Dermatological Diagnostics: A Unified Deep Learning Framework for Skin Lesion and Cancer Classification

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Dermatological Diagnostics: A Unified Deep Learning Framewor...

Advances in Computing, Communication and Networking (ICAC2N), International Conference on

作者： Vinod Kumar Isha Jain Durga Sritha Dongla Shivangi Rai Vani Rastogi Eva Kaushik Rohit Kaushik School of Engineering & Applied Science The George Washington University Washington D.C USA Computer Science & Engineering Department Dr. Akhilesh Das Gupta Institute of Technology and Management New Delhi India Computer Science & Engineering Department Gandhi Institute of Technology and Management Visakhapatnam Andhra Pradesh Data Scientist DXC Technology Noida India CS and Mathematics Department Data Analytics Program University of Illinois Springfield USA

ISBN: (数字)9798350356816

ISBN: (纸本)9798350356823

Skin pathologies encompass a spectrum of conditions, with malignancies such as melanoma representing a critical diagnostic urgency. This investigation delineates the deployment of Convolutional Neural Networks (CNNs) for the classification of dermatological anomalies, benchmarking CNN diagnostic fidelity against dermatological expert evaluations. The study underscores the efficacy of CNN classifiers in expediting the diagnostic workflow for various cutaneous disorders. Advocating for an automated diagnostic framework, the research introduces a CNN-based system aimed at reducing human diagnostic load, accelerating diagnostic timelines, and enhancing survival outcomes. Utilizing advanced image processing algorithms and deep learning architectures, the research presents an automated classification system for skin pathologies, addressing both benign and malignant presentations. The classification matrix includes nine dermatological conditions: actinic keratosis, basal cell carcinoma, benign keratosis, dermatofibroma, melanoma, nevus, seborrheic keratosis, squamous cell carcinoma, and vascular lesions. The objective is to engineer a CNN model with robust diagnostic performance across a diverse lesion dataset, ensuring accurate identification and categorization of dermatological conditions.

关键词： Deep learning Pathology Accuracy Melanoma computer architecture Benchmark testing Skin Convolutional neural networks Lesions Medical diagnosis

Unbiased Estimation of the Vanilla and Deterministic Ensemble Kalman–Bucy Filters

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arXiv 2022年

作者： Álvarez Ballesteros, Miguel Ángel Chada, Neil K. Jasra, Ajay Applied Mathematics and Computational Science Program Computer Electrical and Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology Thuwal23955 Saudi Arabia

In this article we consider the development of an unbiased estimator for the ensemble Kalman–Bucy filter (EnKBF). The EnKBF is a continuous-time filtering methodology which can be viewed as a continuous-time analogue of the famous discrete-time ensemble Kalman filter. Our unbiased estimators will be motivated from recent work [Rhee & Glynn 2010, [31]] which introduces randomization as a means to produce unbiased and finite variance estimators. The randomization enters through both the level of discretization, and through the number of samples at each level. Our estimator will be specific to linear and Gaussian settings, where we know that the EnKBF is consistent, in the particle limit N → ∞, with the KBF. We highlight this for two particular variants of the EnKBF, i.e. the deterministic and vanilla variants, and demonstrate this on a linear Ornstein–Uhlenbeck process. We compare this with the EnKBF and the multilevel (MLEnKBF), for experiments with varying dimension size. We also provide a proof of the multilevel deterministic EnKBF, which provides a guideline for some of the unbiased methods. © 2022, CC BY-NC-SA.

关键词： Continuous time systems

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