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A practical method for computing with piecewise Chebyshevian splines

JOURNAL OF computational AND APPLIED MATHEMATICS 2022年第0期406卷 114051-114051页

作者： Beccari, Carolina Vittoria Casciola, Giulio Romani, Lucia Univ Bologna Dept Math Piazza Porta San Donato 5 I-40126 Bologna Italy

A piecewise Chebyshevian spline space is good for design when it possesses a B-spline basis and this property is preserved under knot insertion. The interest in such kind of spaces is justified by the fact that, similarly as for polynomial splines, the related parametric curves exhibit the desired properties of convex hull inclusion, variation diminution and intuitive relation between the curve shape and the location of the control points. For a good-for-design space, in this paper we construct a set of functions, called transition functions, which allow for efficient computation of the B-spline basis, even in the case of nonuniform and multiple knots. Moreover, we show how the spline coefficients of the representations associated with a refined knot partition and with a raised order can conveniently be expressed by means of transition functions. This result allows us to provide effective procedures that generalize the classical knot insertion and degree raising algorithms for polynomial splines. We further discuss how the approach can straightforwardly be generalized to deal with geometrically continuous piecewise Chebyshevian splines as well as with splines having section spaces of different dimensions. From a numerical point of view, we show that the proposed evaluation method is easier to implement and has higher accuracy than other existing algorithms. (c) 2021 Elsevier B.V. All rights reserved.

关键词： (Piecewise) Chebyshevian splines B-spline basis Knot insertion Order elevation computational algorithms Transition functions

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On some integral equations for the evaluation of first-passage-time densities of time-inhomogeneous birth-death processes

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APPLIED MATHEMATICS AND COMPUTATION 2022年 422卷 126993-126993页

作者： Giorno, Virginia Nobile, Amelia G. Univ Salerno Dipartimento Informat Via Giovanni Paolo II 132 I-84084 Fisciano SA Italy

New integral equations are proposed to determine first-passage-time densities for timeinhomogeneous birth-death processes. Such equations, particularly suitable for computational purposes, are also used to obtain closed-form expressions for the first-passage-time densities of special birth-death processes of interest in various application fields.(c) 2022 Elsevier Inc. All rights reserved.

关键词： First-passage time Polya process Gompertz process M(t)/M(t)/1 Queue M(t)/ M(t)/ Queue computational algorithms

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MCMC-driven importance samplers

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APPLIED MATHEMATICAL MODELLING 2022年 111卷 1-22页

作者： Llorente, F. Curbelo, E. Martino, L. Elvira, V. Delgado, D. Univ Carlos III Madrid UC3M Madrid Spain Univ Rey Juan Carlos URJC Madrid Spain Univ Edinburgh Edinburgh Scotland

Monte Carlo sampling methods are the standard procedure for approximating complicated integrals of multidimensional posterior distributions in Bayesian inference. In this work, we focus on the class of layered adaptive importance sampling algorithms, which is a fam-ily of adaptive importance samplers where Markov chain Monte Carlo algorithms are em-ployed to drive an underlying multiple importance sampling scheme. The modular nature of the layered adaptive importance sampling scheme allows for different possible imple-mentations, yielding a variety of different performances and computational costs. In this work, we propose different enhancements of the classical layered adaptive importance sampling setting in order to increase the efficiency and reduce the computational cost, of both upper and lower layers. The different variants address computational challenges arising in real-world applications, for instance with highly concentrated posterior distri-butions. Furthermore, we introduce different strategies for designing cheaper schemes, for instance, recycling samples generated in the upper layer and using them in the final esti-mators in the lower layer. Different numerical experiments show the benefits of the pro-posed schemes, comparing with benchmark methods presented in the literature, and in several challenging scenarios. (c) 2022 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY-NC-ND license ( http://***/licenses/by-nc-nd/4.0/ )

关键词： Bayesian inference Importance sampling Quadrature methods computational algorithms

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Sensing Approaches and Reconstruction Methods for Improved Lensless Imaging

Sensing Approaches and Reconstruction Methods for Improved L...

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作者： Zheng, Yucheng University of California Riverside

学位级别：Ph.D., Doctor of Philosophy

Lensless imaging systems present a novel alternative to traditional camera designs by replacing the camera lens with a thin, flat, and potentially inexpensive optical encoder, often referred to as a coded mask. This dissertation establishes a framework for the lensless imaging model and explores computational algorithms to extract image and depth information from lensless imaging measurements. The dissertation is organized around three primary areas of focus: Lensless Imaging for 3D Reconstruction Traditionally, estimating the disparity map of a scene requires either capturing a sequence of focus-stacked images or utilizing binocular views with a baseline. However, in lensless imaging, the optical encoder positioned above the camera sensor generates a complex and structured point spread function (PSF) that varies significantly depending on the depth of the light source. This unique property enables the retrieval of depth information from a single frame of measurements. In order to estimate depth maps more accurately on a continuous domain, we formulate the forward imaging model of the system, such that the PSF is represented as a continuous function of depth. Based on this imaging model, we design an alternating update algorithm to jointly estimate the RGB and depth information from the measurements. Improved 3D Lensless Imaging With Learned Programmable Masks Existing methods for lensless imaging can recover both depth and intensity of a scene, but they necessitate solving computationally-intensive inverse problems. Additionally, these methods encounter difficulties when attempting to recover dense scenes with significant depth variations. To address these challenges, we propose a lensless imaging system that captures a limited number of measurements using distinct patterns on a programmable mask. We introduce a fast recovery algorithm, which can be parallelized, to recover textures on a fixed number of depth planes from multiple measurements. Furthermore, we exami

关键词： Lensless imaging systems Optical encoder computational algorithms Point spread function Camera lens

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Evaluation and Prediction of the Hazard Potential Level of Dam Infrastructures Using computational Artificial Intelligence algorithms

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JOURNAL OF MANAGEMENT IN ENGINEERING 2020年第5期36卷

作者： Assaad, Rayan El-adaway, Islam H. Missouri Univ Sci & Technol Dept Civil Architectural & Environm Engn 218 Butler Carlton Hall1401 N Pine St Rolla MO 65409 USA Missouri Univ Sci & Technol Construct Engn & Management 228 Butler Carlton Hall1401 N Pine St Rolla MO 65409 USA Missouri Univ Sci & Technol Civil Engn 228 Butler Carlton Hall1401 N Pine St Rolla MO 65409 USA Missouri Univ Sci & Technol Missouri Consortium Construct Innovat Dept Civil Architectural & Environm Engn 228 Butler Carlton Hall1401 N Pine St Rolla MO 65409 USA Missouri Univ Sci & Technol Dept Engn Management & Syst Engn 228 Butler Carlton Hall1401 N Pine St Rolla MO 65409 USA

Failures of dams cause immense property and environmental damages and take thousands of lives. As such, the goal of this paper is to evaluate and predict the hazard potential level of dams in the US using a comparative approach based on computational artificial intelligence (AI) algorithms. The research methodology comprised data collection from the National Inventory of Dams (NID);data preprocessing;data processing;and model selection and evaluation. To this end, the authors: (1) identified the best subset of variables that affect the prediction of the hazard potential level of dams in the US;(2) investigated the performance of two AI computational algorithms: artificial neural networks (ANNs) and k-nearest neighbors (KNNs) for the evaluation and prediction of the hazard potential levels of US dams;and (3) developed a decision support tool that could be used by the agencies responsible for the management of dams in the US with the capability to predict the hazard potential with good accuracy. The obtained results reflected that the ANN algorithm yielded better accuracy compared to the KNN algorithm. In addition, the conclusions indicated that 19 variables pertaining to dams in the US could affect the hazard potential level of dams. The output is a decision support system that is able to evaluate the hazard potential of dams with a prediction accuracy of 85.70%. This study contributes to the management in engineering's body of knowledge by devising a data-driven framework that is valuable for dams' owners and authorities. Ultimately, the developed computational AI algorithm could be used to evaluate and predict the hazard potential level of US dams with good accuracy while minimizing the efforts, time, and costs associated with formal inspection of the dams. (C) 2020 American Society of Civil Engineers.

关键词： computational algorithms Artificial intelligence (AI) Infrastructure US dams Artificial neural networks (ANNs) k-nearest neighbors (KNNs) Hazard potential Decision support tool

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LN: A Meta-solver for Layered Queueing Network Analysis 19th

LN: A Meta-solver for Layered Queueing Network Analysis

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19th International Conference on Quantitative Evaluation Systems (QEST)

作者： Casale, Giuliano Gao, Yicheng Niu, Zifeng Zhu, Lulai Imperial Coll London Dept Comp London England

ISBN: (纸本)9783031163364;9783031163357

We overview LN, a novel solver introduced in the LINE software package to analyze layered queueing network (LQN) models. The novelty of the LN solver lies in its capability to analyze LQNs with a userdefined combination of solution paradigms, including discrete-event and stochastic simulation, continuous-time Markov chain analysis (CTMC), normalizing constant evaluation (NC), matrix analytic methods (MAM), mean-field approximations (FLUID), and mean-value analysis (MVA). Being parametric in the solver used for each LQN layer, LN as a whole enables the efficient computation of advanced performance metrics such as marginal and joint state probabilities, response and passage time distributions, and transient measures, leveraging individual strengths of the supported solution paradigms. We discuss in particular recent developments added to NC, the default layer solver of LN, which significantly improve the solution of queueing network models obtained using loose layering of the LQN.

关键词： Layered queueing networks computational algorithms Class switching Performance measures

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Choice of an Algorithm for Broadband Monitoring of the Optical Coating Deposition Process Taking into Account the Effect of Error Self-Compensation

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computational Mathematics and Mathematical Physics 2025年第4期65卷 812-824页

作者： Sharov, A. N. Tikhonravov, A. V. Sharapova, S. A. Yagola, A. G. Faculty of Computational Mathematics and Cybernetics Shenzhen MSU-BIT University Shenzhen China Faculty of Physics Lomonosov Moscow State University Moscow Russia Research Computing Center Lomonosov Moscow State University Moscow Russia Moscow Center for Fundamental and Applied Mathematics Moscow Russia

Two algorithms of broadband optical monitoring of the optical coating deposition process are considered both without solving the additional inverse problem of refining the thicknesses of the already deposited layers and with its solution. It is shown that refining the thicknesses of the already deposited layers leads to a decrease in errors of the thicknesses of the layers but does not always provide a more accurate implementation of the required spectral properties of the coating. For the first time, it is demonstrated that when choosing a monitoring algorithm, the effect of error self-compensation should be taken into account.

关键词： mathematical modelling computational algorithms inverse problems optical coatings coating deposition broadband monitoring error correlation error self-compensation

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Construction and computation of unified Stirling-type numbers emerging from p-adic integrals and symmetric polynomials

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REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS 2021年第4期115卷 1-24页

作者： Kucukoglu, Irem Simsek, Yilmaz Alanya Alaaddin Keykubat Univ Dept Engn Fundamental Sci Fac Engn TR-07425 Antalya Turkey Univ Akdeniz Dept Math Fac Sci TR-07058 Antalya Turkey

The aim of this paper is to give construction and computation methods for generalized and unified representations of Stirling-type numbers and Bernoulli-type numbers and polynomials. Firstly, we define generalized and unified representations of the falling factorials. By using these new representations as components of the generating functions, we also construct generalized and unified representations of Stirling-type numbers. By making use of the symmetric polynomials, we give computational formulas and algorithm for these numbers. Applying Riemann integral to the unified falling factorials, we introduce new families of Bernoulli-type numbers and polynomials of the second kind by their computation formulas and plots drawn by the Wolfram programming language in Mathematica. Applying p-adic integrals to the unified falling factorials, we construct two new sequences that involve some well-known special numbers such as the Stirling numbers, the Bernoulli numbers and the Euler numbers. Finally, we give not only further remarks and observations, but also some open questions regarding the potential applications and relations of our results.

关键词： Factorial polynomials Bernoulli and Euler numbers Stirling numbers Symmetric polynomials Catalan numbers Central factorial numbers computational formulas computational algorithms p-adic integrals

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Probabilistic forecasting using deep generative models

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GEOINFORMATICA 2021年第1期25卷 127-147页

作者： Fanfarillo, Alessandro Roozitalab, Behrooz Hu, Weiming Cervone, Guido Natl Ctr Atmospher Res Res Applicat Lab POB 3000 Boulder CO 80307 USA Univ Iowa Dept Chem & Biochem Engn Iowa City IA 52242 USA Univ Iowa Ctr Global & Reg Environm Res Iowa City IA USA Penn State Univ Dept Geog State Coll PA USA Penn State Univ Inst CyberSci Geoinformat & Earth Observat Lab State Coll PA USA

A fundamental problem in Numerical Weather Prediction (NWP) is the generation of ensembles to capture the probability of future states of the atmosphere. This research presents a new methodology to generate analogs using deep generative models, an emerging class of deep learning approaches. The goal is to train a deep generative model using a set of historical forecasts and associated observations, and to use it to entirely or partially replace the need to maintain a potentially very large dataset. In this research, this new methodology is compared with the Analog Ensemble (AnEn) approach, a computationally efficient solution to generate analogs. The proposed approach promises to reduce the amount of memory required to produce the probabilistic forecast by several orders of magnitude. Results show that the generative model solution is constant time without performing any search, saving a considerable amount of time even in the presence of huge historical datasets.

关键词： computational algorithms Ensemble modeling Deep learning

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Network on chip for enterprise information management and integration in intelligent physical systems

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ENTERPRISE INFORMATION SYSTEMS 2021年第7期15卷 935-950页

作者： Chen, Guobin Li, Shijin Rongzhi Coll Chongqing Technol & Business Univ Chongqing Key Lab Spatial Data Min & Big Data Int Chongqing Peoples R China Yunnan Univ Finance & Econ Acad Affairs Off Kunming Yunnan Peoples R China

Recently, solution of discretisation operator technique with circular (DOTWC) approach, and runge-kutta implicit are presented for the Eigen efficient analysis, in this paper based on the various surveys it has been analysed that the efficiency is considered as low and computational burden terms to be high. Henceforth, the implicitly of the restarted Arnoldi (IRA) with intelligent physical system (IPS) with IOT algorithm is implemented for the computational Eigenvalues of critical solution operators in discretized matrices to optimise efficiency and computational burden. Furthermore, we have proposed the Advancement Deep Learning Reinforcement (ADLR) algorithms to improve the efficiency and existing of scalability of the intelligent physical system.

关键词： Eigen Efficient Analysis ira computational algorithms intelligent Physical System and Deep Learning Reinforcement

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