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Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms

作者： Karen Daniels Victor J. Milenkovic Harvard University Division of Applied Sciences University of Miami Department of Math and Computer Science

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The δ- sensitivity and its application to stochastic optimal control of nonlinear diffusions.

The δ- sensitivity and its application to stochastic optima...

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American Control Conference

作者： Evangelos A. Theodorou Emo Todorov the Department of Computer Science and Engineering University of Washington Seattle. Departments of Computer Science and Engineering and Applied Math University of Washington

ISBN: (纸本)9781479901777

We provide optimal control laws by using tools from stochastic calculus of variations and the mathematical concept of δ-sensitivity. The analysis relies on logarithmic transformations of the value functions and the use of linearly solvable Partial Differential Equations(PDEs). We derive the corresponding optimal control as a function of the δ-sensitivity of the logarithmic transformation of the value function for the case of nonlinear diffusion processes affine in control and noise.

关键词： nonlinear diffusions PDEs value functions

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Calcination Temperature-Dependent Structural and Photoluminescence Properties of Hydroxyapatite Derived from Labeo Rohita Fish Scales

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Journal of The Institution of Engineers (India): Series D 2020年第2期101卷 223-232页

作者： Sinha, Arijit Pal, Anindya Santra, A. Murmu, S. Ghorai, U.K. Chowdhury, Amit Roy Banerjee, D. Dr. M.N. Dastur School of Materials Science Engineering Indian Institute of Engineering Science and Technology Botanic Garden Shibpur Howrah711103 India Ramakrishna Mission Vidyamandira Department of Industrial Chemistry & Applied Chemistry Swami Vivekananada Research Centre Belur Math Howrah711202 India Aerospace Engineering and Applied Mechanics Indian Institute of Engineering Science and Technology Botanic Garden Shibpur Howrah711103 India Faculty of Engineering and Computer Science Teerthanker Mahaveer University MoradabadUP244001 India

The nanocrystalline hydroxyapatite was synthesized from Labeo Rohita fish scales by calcination of raw scales at temperatures ranges from 400 to 1000 °C. The synthesized powders were characterized using, X-ray diffraction (XRD), thermogravimetric/differential thermal analyzer (TG–DTA), Fourier transform infrared spectroscopy, scanning and high-resolution transmission electron microscope and energy-dispersive X-ray analysis, respectively. Crystallite size, crystallinity and lattice parameters of HAp were evaluated from XRD, and it is shown that the average crystallite sizes were significantly enhanced with the calcination temperature attending its maximum value at ~ 40 nm. TG–DTA analysis predicts the thermal stability of the samples, and it has been observed that the thermal stability increases with the calcination temperature. Moreover, a detailed photoluminescence study of the as-synthesized samples has been carried out for the first time and an appropriate excitation energy gives rise to several distinct peaks in the emission spectra which has not been reported previously. © 2020, The Institution of Engineers (India).

关键词： Optical properties

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Stochastic Optimal Control for Nonlinear Markov Jump Diffusion Processes

Stochastic Optimal Control for Nonlinear Markov Jump Diffusi...

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American Control Conference

作者： Evangelos A. Theodorou Emmanuel Todorov Department of Computer Science and Engineering University of Washington Seattle USA Department of Computer Science and Engineering and Department of Applied Math University of Washington Seattle USA

ISBN: (纸本)9781457710957

We consider the problem finite horizon stochastic optimal control for nonlinear markov jump diffusion processes. In particular, by using stochastic calculus for markov jump diffusions processes and the logarithmic transformation of the value function we demonstrate the transformation of the corresponding Hamilton-Jacobi-Bellman (HJB) Partial Differential Equation (PDE) to the backward Chapman Kolmogorov PDE for jump diffusions. Furthermore we derive the Feynman-Kac lemma for nonlinear markov jump diffusions processes and apply it to the transformed HJB equation. Application of the Feynman-Kac lemma yields the solution of the transformed HJB equation. The path integral interpretation is derived. Finally, conclusions and future directions are discussed.

关键词： jump Markov stochastic optimal control logarithmic transformation diffusion Diffusion processes Lemma

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Adjoint-Free 4D-Var Methods Via Line Search Optimization For Non-Linear Data Assimilation

arXiv

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arXiv 2023年

作者： Nino-Ruiz, Elias D. Diaz-Rodriguez, Jairo Applied Math and Computer Science Laboratory Department of Computer Science Universidad del Norte Colombia Department of Mathematics and Statistics York University Canada

This paper proposes two practical implementations of Four-Dimensional Variational (4D-Var) Ensemble Kalman Filter (4D-EnKF) methods for non-linear data assimilation. Our formulations' main idea is to avoid the intrinsic need for adjoint models in the context of 4D-Var optimization and, even more, to handle non-linear observation operators during the assimilation of observations. The proposed methods work as follows: snapshots of an ensemble of model realizations are taken at observation times, these snapshots are employed to build control spaces onto which analysis increments can be estimated. Via the linearization of observation operators at observation times, a line-search based optimization method is proposed to estimate optimal analysis increments. The convergence of this method is theoretically proven as long as the dimension of control-spaces equals model one. In the first formulation, control spaces are given by full-rank square root approximations of background error covariance matrices via the Bickel and Levina precision matrix estimator. In this context, we propose an iterative Woodbury matrix formula to perform the optimization steps efficiently. The last formulation can be considered as an extension of the Maximum Likelihood Ensemble Filter to the 4D-Var context. This employs pseudo-square root approximations of prior error covariance matrices to build control spaces. Experimental tests are performed by using the Lorenz 96 model. The results reveal that, in terms of Root-Mean-Square-Error values, both methods can obtain reasonable estimates of posterior error modes in the 4D-Var optimization problem. Moreover, the accuracies of the proposed filter implementations can be improved as the ensemble sizes are increased. © 2023, CC BY.

关键词： Optimization

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A new trigonometric kernel function for support vector machine

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Iran Journal of computer science 2023年第2期6卷 137-145页

作者： Fathi Hafshejani, Sajad Moaberfard, Zahra Department of Applied Mathematics Shiraz University of Technology Modarres Boulevard Fars Shiraz 71557-13876 Iran Department of Math and Computer Science University of Lethbridge 4401 University Dr W Lethbridge T1K 3M4 AB Canada

In the last few years, various types of machine learning algorithms, such as support vector machine (SVM), support vector regression (SVR), and non-negative matrix factorization (NMF) have been introduced. The kernel approach is an effective method for increasing the classification accuracy of machine learning algorithms. This paper introduces a family of one-parameter kernel functions for improving the accuracy of SVM classification. The proposed kernel function consists of a trigonometric term and differs from all existing kernel functions. We show this function is a positive definite kernel function. Finally, we evaluate the SVM method based on the new trigonometric kernel, the Gaussian kernel, the polynomial kernel, and a convex combination of the new kernel function and the Gaussian kernel function on various types of datasets. Empirical results show that the SVM based on the new trigonometric kernel function and the mixed kernel function achieve the best classification accuracy. Moreover, some numerical results of performing the SVR based on the new trigonometric kernel function and the mixed kernel function are presented. © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2022.

关键词： Kernel method Support vector machine Trigonometric kernel function

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Private Everlasting Prediction

arXiv

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arXiv 2023年

作者： Naor, Moni Nissim, Kobbi Stemmer, Uri Yan, Chao Department of Computer Science and Applied Math Weizmann Institute of Science Blavatnik School of Computer Science Tel Aviv University Google Research Department of Computer Science Georgetown University United States

A private learner is trained on a sample of labeled points and generates a hypothesis that can be used for predicting the labels of newly sampled points while protecting the privacy of the training set [Kasiviswannathan et al., FOCS 2008]. Research uncovered that private learners may need to exhibit significantly higher sample complexity than non-private learners as is the case with, e.g., learning of one-dimensional threshold functions [Bun et al., FOCS 2015, Alon et al., STOC 2019]. We explore prediction as an alternative to learning. Instead of putting forward a hypothesis, a predictor answers a stream of classification queries. Earlier work has considered a private prediction model with just a single classification query [Dwork and Feldman, COLT 2018]. We observe that when answering a stream of queries, a predictor must modify the hypothesis it uses over time, and, furthermore, that it must use the queries for this modification, hence introducing potential privacy risks with respect to the queries themselves. We introduce private everlasting prediction taking into account the privacy of both the training set and the (adaptively chosen) queries made to the predictor. We then present a generic construction of private everlasting predictors in the PAC model. The sample complexity of the initial training sample in our construction is quadratic (up to polylog factors) in the VC dimension of the concept class. Our construction allows prediction for all concept classes with finite VC dimension, and in particular threshold functions with constant size initial training sample, even when considered over infinite domains, whereas it is known that the sample complexity of privately learning threshold functions must grow as a function of the domain size and hence is impossible for infinite domains. Copyright © 2023, The Authors. All rights reserved.

关键词： Forecasting

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A graph-based convolutional neural network stock price prediction with leading indicators

A graph-based convolutional neural network stock price predi...

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作者： Wu, Jimmy Ming-Tai Li, Zhongcui Srivastava, Gautam Tasi, Meng-Hsiun Lin, Jerry Chun-Wei College of Computer Science and Engineering Shandong University of Science and Technology Shandong China Department of Math and Computer Science Brandon University Brandon Canada Research Centre for Interneural Computing China Medical University Taichung Taiwan Department of Management Information Systems National Chung Hsing University Taichung Taiwan Department of Computer Science Electrical Engineering and Mathematical Sciences Western Norway University of Applied Sciences Bergen Norway

The stock market is a capitalistic haven where the issued shares are transferred, traded, and circulated. It bases stock prices on the issue market, however, the structure and trading activities of the stock market are much more complicated than the issue market itself. Therefore, making an accurate prediction becomes an intricate as well as highly difficult task. On the other hand, because of the potential benefits of stock prediction, it attracts generation after generation of scholars as well as investors to continuously develop various prediction methods from different perspectives, a myriad of theories, a multitude of investment strategies, and different practical experiences. In this article, aiming at the task of time series (financial) feature extraction and prediction of price movements, a new convolutional novel neural network that can be called a framework to improve the prediction accuracy of stock trading is proposed. The method that is proposed is called SSACNN, a short form of stock sequence array convolutional neural network. SSACNN collects data including historical data of prices and its leading indicators (options/futures) for a stock to take an array as the input graph of the convolutional neural network framework. In our experimental results, five Taiwanese and American stocks were used as a benchmark to compare with the previous algorithms and proposed algorithm, the motion prediction performance of SSACNN has been improved significantly and proved that it has the potential to be applied in the real financial market. © 2020 John Wiley & Sons Ltd

关键词： Forecasting

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Heavy hitters and the structure of local privacy

arXiv

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arXiv 2017年

作者： Bun, Mark Nelson, Jelani Stemmer, Uri Department of Computer Science Princeton University John A. Paulson School of Engineering and Applied Sciences Harvard University Dept. of Computer Science and Applied Math Weizmann Institute of Science

We present a new locally differentially private algorithm for the heavy hitters problem which achieves optimal worst-case error as a function of all standardly considered parameters. Prior work obtained error rates which depend optimally on the number of users, the size of the domain, and the privacy parameter, but depend sub-optimally on the failure probability. We strengthen existing lower bounds on the error to incorporate the failure probability, and show that our new upper bound is tight with respect to this parameter as well. Our lower bound is based on a new understanding of the structure of locally private protocols. We further develop these ideas to obtain the following general results beyond heavy hitters. Advanced Grouposition: In the local model, group privacy for k users degrades proportionally to ≈ √k, instead of linearly in k as in the central model. Stronger group privacy yields improved max-information guarantees, as well as stronger lower bounds (via "packing arguments"), over the central model. Building on a transformation of Bassily and Smith (STOC 2015), we give a generic transformation from any non-interactive approximate-private local protocol into a pure-private local protocol. Again in contrast with the central model, this shows that we cannot obtain more accurate algorithms by moving from pure to approximate local privacy. Copyright © 2017, The Authors. All rights reserved.

关键词： Errors

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Adaptive particle swarm optimization model for resource leveling

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Evolving Systems 2023年第4期14卷 593-604页

作者： Lin, Jerry Chun-Wei Lv, Qing Yu, Dehu Srivastava, Gautam Chen, Chun-Hao School of Information and Control Engineering Qingdao University of Technology Qingdao China Department of Computer Science Electrical Engineering and Mathematical Sciences Western Norway University of Applied Sciences Bergen Norway School of Civil Engineering Qingdao University of Technology Qingdao China School of Civil Engineering Shandong Jianzhu University Jinan China Department of Math and Computer Science Brandon University Brandon Canada Research Centre for Interneural Computing China Medical University Taichung Taiwan Department of Information and Finance Management National Taipei University of Technology Taipei Taiwan

In the process of engineering project construction, the balanced allocation of resources has an important impact on the purchase of actual materials, the progress of the site construction and the arrangement of temporary facilities. Although there have been many studies on the use of evolutionary computation (EC) to solve the fixed duration of the resource-leveling problem, the optimization effect of standard EC to solve the resource-balancing problem in large-scale network design planning is reduced due to the phenomenon of premature convergence of PSO and the complexity of large-scale network planning. Therefore, in this paper, an adaptive dissipative particle swarm optimization (ADPSO) algorithm is used to solve the resource balancing optimization problem for different network-plans scales, and the feasibility of the developed model is verified using four different scaled network plans (databases). At the same time, a solution to the dynamic resource-leveling problem with optimization for a fixed duration is proposed. The results show that the proposed models are suitable for solving the problem of resource-leveling with a fixed duration of optimization of different scale network plans, and their accuracy and stability are significantly improved compared to the state-of-the-art approaches. Moreover, the proposed models are accurate and suitable for combining the calculation method of network planning time parameters with the ADPSO algorithm to realize dynamic resource balancing optimization. © 2022, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.

关键词： Particle swarm optimization (PSO)

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